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Showing papers on "Nonlinear programming published in 2016"


01 Jan 2016
TL;DR: The linear and nonlinear programming is universally compatible with any devices to read and is available in the book collection an online access to it is set as public so you can download it instantly.
Abstract: Thank you for downloading linear and nonlinear programming. As you may know, people have search numerous times for their favorite novels like this linear and nonlinear programming, but end up in malicious downloads. Rather than reading a good book with a cup of tea in the afternoon, instead they juggled with some infectious bugs inside their desktop computer. linear and nonlinear programming is available in our book collection an online access to it is set as public so you can download it instantly. Our digital library spans in multiple locations, allowing you to get the most less latency time to download any of our books like this one. Kindly say, the linear and nonlinear programming is universally compatible with any devices to read.

943 citations


Journal Article
TL;DR: CVXPY as mentioned in this paper is a domain-specific language for convex optimization embedded in Python, which allows the user to express convex optimisation problems in a natural syntax that follows the math, rather than in the restrictive standard form required by solvers.
Abstract: CVXPY is a domain-specific language for convex optimization embedded in Python. It allows the user to express convex optimization problems in a natural syntax that follows the math, rather than in the restrictive standard form required by solvers. CVXPY makes it easy to combine convex optimization with high-level features of Python such as parallelism and object-oriented design. CVXPY is available at http://www.cvxpy.org/ under the GPL license, along with documentation and examples.

873 citations


Journal ArticleDOI
TL;DR: This paper describes a collection of optimization algorithms for achieving dynamic planning, control, and state estimation for a bipedal robot designed to operate reliably in complex environments and presents a state estimator formulation that permits highly precise execution of extended walking plans over non-flat terrain.
Abstract: This paper describes a collection of optimization algorithms for achieving dynamic planning, control, and state estimation for a bipedal robot designed to operate reliably in complex environments. To make challenging locomotion tasks tractable, we describe several novel applications of convex, mixed-integer, and sparse nonlinear optimization to problems ranging from footstep placement to whole-body planning and control. We also present a state estimator formulation that, when combined with our walking controller, permits highly precise execution of extended walking plans over non-flat terrain. We describe our complete system integration and experiments carried out on Atlas, a full-size hydraulic humanoid robot built by Boston Dynamics, Inc.

715 citations


Journal ArticleDOI
TL;DR: This work investigates the convex–concave procedure, a local heuristic that utilizes the tools of convex optimization to find local optima of difference of conveX (DC) programming problems, and generalizes the algorithm to include vector inequalities.
Abstract: We investigate the convex–concave procedure, a local heuristic that utilizes the tools of convex optimization to find local optima of difference of convex (DC) programming problems. The class of DC problems includes many difficult problems such as the traveling salesman problem. We extend the standard procedure in two major ways and describe several variations. First, we allow for the algorithm to be initialized without a feasible point. Second, we generalize the algorithm to include vector inequalities. We then present several examples to demonstrate these algorithms.

650 citations


01 Jan 2016
TL;DR: In this article, a convex mathematical programming problem in which the usual definition of the feasible region is replaced by a significantly different strategy is defined via set containment, where instead of specifying the feasible regions by a set of convex inequalities,fi(x)_ bi, i=1, 2,, m, the feasible area is defined by set containment.
Abstract: This note formulates a convex mathematical programming problem in which the usual definition of the feasible region is replaced by a significantly different strategy. Instead of specifying the feasible region by a set of convex inequalities,fi(x)_ bi, i=1, 2, , m, the feasible region is defined via set containment. Here n convex activity sets {Kj, j=1, 2, * * *, n} and a convex resource set K are specified and the feasible region is given by

628 citations


Journal ArticleDOI
TL;DR: The AG method is generalized to solve nonconvex and possibly stochastic optimization problems and it is demonstrated that by properly specifying the stepsize policy, the AG method exhibits the best known rate of convergence for solving general non Convex smooth optimization problems by using first-order information, similarly to the gradient descent method.
Abstract: In this paper, we generalize the well-known Nesterov's accelerated gradient (AG) method, originally designed for convex smooth optimization, to solve nonconvex and possibly stochastic optimization problems. We demonstrate that by properly specifying the stepsize policy, the AG method exhibits the best known rate of convergence for solving general nonconvex smooth optimization problems by using first-order information, similarly to the gradient descent method. We then consider an important class of composite optimization problems and show that the AG method can solve them uniformly, i.e., by using the same aggressive stepsize policy as in the convex case, even if the problem turns out to be nonconvex. We demonstrate that the AG method exhibits an optimal rate of convergence if the composite problem is convex, and improves the best known rate of convergence if the problem is nonconvex. Based on the AG method, we also present new nonconvex stochastic approximation methods and show that they can improve a few existing rates of convergence for nonconvex stochastic optimization. To the best of our knowledge, this is the first time that the convergence of the AG method has been established for solving nonconvex nonlinear programming in the literature.

578 citations


Journal ArticleDOI
TL;DR: This paper represents an attempt to apply second-order cone programming, a branch of convex optimization, to the class of highly nonlinear trajectory optimization problems in entry flight with a combination of successive linearization and relaxation techniques.
Abstract: Convex optimization has found wide applications in recent years due to its unique theoretical advantages and the polynomial-time complexity of state-of-the-art solution algorithms for convex programming This paper represents an attempt to apply second-order cone programming, a branch of convex optimization, to the class of highly nonlinear trajectory optimization problems in entry flight The foremost challenge in applying convex optimization in most aerospace engineering problems lies in the nonlinearity and nonconvexity of the problem Exclusive reliance on linearization does not always work well, as is the case in entry trajectory optimization This paper focuses on how to formulate realistic, highly constrained entry trajectory optimization problems in a fashion suitable to be solved by second-order cone programming with a combination of successive linearization and relaxation techniques Rigorous analysis is conducted to support the soundness of the approach Numerical demonstrations are provided to

210 citations


Proceedings ArticleDOI
16 May 2016
TL;DR: This paper presents a methodology that allows for the fast and reliable generation of efficient multi-contact robotic walking gaits through the framework of HZD, even in the presence of underactuation, and experimentally validated the methodology on the spring-legged prototype humanoid, DURUS, showing that the optimization approach yields dynamic and stable 3D walking Gaits.
Abstract: Hybrid zero dynamics (HZD) has emerged as a popular framework for dynamic and underactuated bipedal walking, but has significant implementation difficulties when applied to the high degrees of freedom present in humanoid robots. The primary impediment is the process of gait design-it is difficult for optimizers to converge on a viable set of virtual constraints defining a gait. This paper presents a methodology that allows for the fast and reliable generation of efficient multi-contact robotic walking gaits through the framework of HZD, even in the presence of underactuation. To achieve this goal, we unify methods from trajectory optimization with the control framework of multi-domain hybrid zero dynamics. By formulating a novel optimization problem in the context of direct collocation and generating analytic Jacobians for the constraints, solving the resulting nonlinear program becomes tractable for large-scale nonlinear programming solvers, even for systems as high-dimensional as humanoid robots. We experimentally validated our methodology on the spring-legged prototype humanoid, DURUS, showing that the optimization approach yields dynamic and stable 3D walking gaits.

205 citations


Journal ArticleDOI
01 Mar 2016
TL;DR: Comparison of obtained computation results with those of several recent meta-heuristic algorithms shows the superiority of the IAPSO in terms of accuracy and convergence speed.
Abstract: Flowchart of the improved accelerated particle swarm optimization. A new improved accelerated particle swarm optimization algorithm is proposed (IAPSO).Individual particles memories are incorporated in order to increase swarm diversity.Balance between exploration and exploitation is controlled through two selected functions.IAPSO outperforms several recent meta-heuristic algorithms, in terms of accuracy and convergence speed.New optimal solutions, for some benchmark engineering problems, are obtained. This paper introduces an improved accelerated particle swarm optimization algorithm (IAPSO) to solve constrained nonlinear optimization problems with various types of design variables. The main improvements of the original algorithm are the incorporation of the individual particles memories, in order to increase swarm diversity, and the introduction of two selected functions to control balance between exploration and exploitation, during search process. These modifications are used to update particles positions of the swarm. Performance of the proposed algorithm is illustrated through six benchmark mechanical engineering design optimization problems. Comparison of obtained computation results with those of several recent meta-heuristic algorithms shows the superiority of the IAPSO in terms of accuracy and convergence speed.

195 citations


Journal ArticleDOI
TL;DR: This work provides a comprehensive and detailed literature review in terms of significant theoretical contributions, algorithmic developments, software implementations and applications for both MINLP and CDFO, and shows their individual prerequisites, formulations and applicability.

195 citations


Journal ArticleDOI
TL;DR: It is proved that the proposed design can solve the exact optimization problem with rejecting disturbances and is proposed a distributed optimization controller for heterogeneous and nonlinear agents in the form of continuous-time minimum-phase systems with unity relative degree.
Abstract: The paper studies the distributed optimization problem for a class of nonlinear multiagent systems in the presence of external disturbances. To solve the problem, we need to achieve the optimal multiagent consensus based on local cost function information and neighboring information and meanwhile to reject local disturbance signals modeled by an exogenous system. With convex analysis and the internal model approach, we propose a distributed optimization controller for heterogeneous and nonlinear agents in the form of continuous-time minimum-phase systems with unity relative degree. We prove that the proposed design can solve the exact optimization problem with rejecting disturbances.

Journal ArticleDOI
TL;DR: In this paper, a two-stage distributionally robust optimization model for the joint energy and reserve dispatch (D-RERD for short) of bulk power systems with significant renewable energy penetration is proposed.
Abstract: This paper proposes a two-stage distributionally robust optimization model for the joint energy and reserve dispatch (D-RERD for short) of bulk power systems with significant renewable energy penetration. Distinguished from the prevalent uncertainty set-based and worst-case scenario oriented robust optimization methodology, we assume that the output of volatile renewable generation follows some ambiguous distribution with known expectations and variances, the probability distribution function (pdf) is restricted in a functional uncertainty set. D-RERD aims at minimizing the total expected production cost in the worst renewable power distribution. In this way, D-RERD inherits the advantages from both stochastic optimization and robust optimization: statistical characteristic is taken into account in a data-driven manner without requiring the exact pdf of uncertain factors. We present a convex optimization-based algorithm to solve the D-RERD, which involves solving semidefinite programming (SDP), convex quadratic programming (CQP), and linear programming (LP). The performance of the proposed approach is compared with the emerging adaptive robust optimization (ARO)-based model on the IEEE 118-bus system. Their respective features are discussed in case studies.

Posted Content
TL;DR: A major theme of this study is that large-scale machine learning represents a distinctive setting in which the stochastic gradient method has traditionally played a central role while conventional gradient-based nonlinear optimization techniques typically falter, leading to a discussion about the next generation of optimization methods for large- scale machine learning.
Abstract: This paper provides a review and commentary on the past, present, and future of numerical optimization algorithms in the context of machine learning applications. Through case studies on text classification and the training of deep neural networks, we discuss how optimization problems arise in machine learning and what makes them challenging. A major theme of our study is that large-scale machine learning represents a distinctive setting in which the stochastic gradient (SG) method has traditionally played a central role while conventional gradient-based nonlinear optimization techniques typically falter. Based on this viewpoint, we present a comprehensive theory of a straightforward, yet versatile SG algorithm, discuss its practical behavior, and highlight opportunities for designing algorithms with improved performance. This leads to a discussion about the next generation of optimization methods for large-scale machine learning, including an investigation of two main streams of research on techniques that diminish noise in the stochastic directions and methods that make use of second-order derivative approximations.

01 Jan 2016
TL;DR: The nonlinear programming analysis and methods is universally compatible with any devices to read and is available in the book collection an online access to it is set as public so you can get it instantly.
Abstract: Thank you for downloading nonlinear programming analysis and methods. As you may know, people have search numerous times for their chosen novels like this nonlinear programming analysis and methods, but end up in malicious downloads. Rather than enjoying a good book with a cup of tea in the afternoon, instead they cope with some infectious virus inside their laptop. nonlinear programming analysis and methods is available in our book collection an online access to it is set as public so you can get it instantly. Our book servers saves in multiple countries, allowing you to get the most less latency time to download any of our books like this one. Merely said, the nonlinear programming analysis and methods is universally compatible with any devices to read.

Journal ArticleDOI
TL;DR: This article describes a complete and concise basis of knowledge for beginning OPF research, tailored for the operations researcher who has experience with nonlinear optimization but little knowledge of electrical engineering.
Abstract: The set of optimization problems in electric power systems engineering known collectively as Optimal Power Flow (OPF) is one of the most practically important and well-researched subfields of const...

Journal ArticleDOI
TL;DR: A parallelizable method is proposed that combines ideas from the fields of sequential quadratic programming and augmented Lagrangian algorithms that negotiates shared dual variables that may be interpreted as prices, a concept employed in dual decomposition methods and the alternating direction method of multipliers (ADMM).
Abstract: This paper is about distributed derivative-based algorithms for solving optimization problems with a separable (potentially nonconvex) objective function and coupled affine constraints. A parallelizable method is proposed that combines ideas from the fields of sequential quadratic programming and augmented Lagrangian algorithms. The method negotiates shared dual variables that may be interpreted as prices, a concept employed in dual decomposition methods and the alternating direction method of multipliers (ADMM). Here, each agent solves its own small-scale nonlinear programming problem and communicates with other agents by solving coupled quadratic programming problems. These coupled quadratic programming problems have equality constraints for which parallelizable methods are available. The use of techniques associated with standard sequential quadratic programming methods gives a method with superlinear or quadratic convergence rate under suitable conditions. This is in contrast to existing decomposition...

Journal ArticleDOI
TL;DR: A fast NMPC algorithm implemented on a field-programmable gate array (FPGA) that employs a particle swarm optimization (PSO) algorithm to handle nonlinear optimization and achieves satisfactory control performance is presented.
Abstract: Nonlinear model predictive control (NMPC) requires a repeated online solution of a nonlinear optimal control problem. The computation load remains the main challenge for the real-time practical application of the NMPC technique, particularly for fast systems. This paper presents a fast NMPC algorithm implemented on a field-programmable gate array (FPGA) that employs a particle swarm optimization (PSO) algorithm to handle nonlinear optimization. The FPGA is used to explore the possibilities of parallel architecture for the substantial acceleration of NMPC. PSO is employed to achieve real-time operation due to its naturally parallel capabilities. The proposed FPGA-based NMPC-PSO controller consists of a random-number generator, a fixed-point arithmetic, a PSO solver, and a universal asynchronous receiver/transmitter communication interface. Then, this controller is applied to an engine idle speed control problem and demonstrated with an FPGA-in-the-loop testbench. The experimental results indicate that the NMPC-on-FPGA-chip strategy has good computational performance and achieves satisfactory control performance.

Journal ArticleDOI
TL;DR: The SEISCOPE optimization toolbox is a set of FORTRAN 90 routines, which implement first- order methods and second-order methods, for the solution of large-scale nonlinear optimization problems, including Traveltime tomography, least-squares migration, or full-waveform inversion.
Abstract: The SEISCOPE optimization toolbox is a set of FORTRAN 90 routines, which implement first-order methods (steepest-descent and nonlinear conjugate gradient) and second-order methods (l-BFGS and truncated Newton), for the solution of large-scale nonlinear optimization problems. An efficient line-search strategy ensures the robustness of these implementations. The routines are proposed as black boxes easy to interface with any computational code, where such large-scale minimization problems have to be solved. Traveltime tomography, least-squares migration, or full-waveform inversion are examples of such problems in the context of geophysics. Integrating the toolbox for solving this class of problems presents two advantages. First, it helps to separate the routines depending on the physics of the problem from the ones related to the minimization itself, thanks to the reverse communication protocol. This enhances flexibility in code development and maintenance. Second, it allows us to switch easily betw...

Proceedings ArticleDOI
06 Jul 2016
TL;DR: A fast optimization algorithm for approximately minimizing convex quadratic functions over the intersection of affine and separable constraints (i.e., the Cartesian product of possibly nonconvex real sets) that is based on a variation of the alternating direction method of multipliers (ADMM).
Abstract: In this paper we propose a fast optimization algorithm for approximately minimizing convex quadratic functions over the intersection of affine and separable constraints (i.e., the Cartesian product of possibly nonconvex real sets). This problem class contains many NP-hard problems such as mixed-integer quadratic programming. Our heuristic is based on a variation of the alternating direction method of multipliers (ADMM), an algorithm for solving convex optimization problems. We discuss the favorable computational aspects of our algorithm, which allow it to run quickly even on very modest computational platforms such as embedded processors. We give several examples for which an approximate solution should be found very quickly, such as management of a hybrid-electric vehicle drivetrain. Our numerical experiments suggest that our method is very effective in finding a feasible point with small objective value; indeed, we see that in many cases, it finds the global solution.

Journal ArticleDOI
TL;DR: In this article, a convex optimization technique called second order cone programming (SOCP) relaxation is applied to obtain the globally optimal solution and avoid the problem of NP-hardness.
Abstract: In this paper, distributed energy storage (DES) devices, like batteries and ultra-capacitors, are used to alleviate detrimental impacts of high penetration photovoltaic (PV) resources on distribution systems. The impacts are studied at mainly two time resolutions—one minute and one hour. To determine accurately the size of the required DES for the purpose of mitigating the impacts of large-scale distributed PV, sizing procedures based on OpenDSS are proposed. After determining the total size of the required DES, optimization techniques can be used to choose the optimal locations for the DES along the feeder, which is a continuous optimization problem taking into account equality constraints of the AC power flow. The continuity of the problem and the radial network structure make it possible to apply a convex optimization technique called second order cone programming (SOCP) relaxation to obtain the globally optimal solution and avoid the problem of NP-hardness. The exactness of the introduced SOCP relaxation is sensitive to the chosen objective function and additional quadratic equalities. The necessary and sufficient condition of exactness for the SOCP relaxation of the DES optimal allocation and operation in radial distribution systems is studied. The proposed methods are applied to an actual feeder in the southwestern US with high penetration of PV using actual measured data. The simulation results demonstrate the efficacy of the proposed approaches.

Journal ArticleDOI
TL;DR: The proposed sub‐optimal strategy is compared with the optimal solution provided by dynamic programming for validation purposes and it is shown that the low computational load of the presented approach enables robustness properties and results very appealing for online use.
Abstract: The problem of eco-driving is analyzed for an urban traffic network in presence of signalized intersections. It is assumed that the traffic lights timings are known and available to the vehicles via infrastructure-to-vehicle (I2V) communication. This work provides a solution to the energy consumption minimization, while traveling through a sequence of signalized intersections and always catching a green light. The optimal control problem is non-convex due to the constraints coming from the traffic lights, therefore a sub-optimal strategy to restore the convexity and solve the problem is proposed. Firstly, a pruning algorithm aims at reducing the optimization domain, by considering only the portions of the traffic lights green phases that allow to drive in compliance with the city speed limits. Then, a graph is created in the feasible region, in order to approximate the energy consumption associated with each available path in the driving horizon. Lastly, after the problem convexity is recovered, a simple optimization problem is solved on the selected path to calculate the optimal crossing times at each intersection. The optimal speeds are then suggested to the driver. The proposed sub-optimal strategy is compared to the optimal solution provided by Dynamic Programming, for validation purposes. It is also shown that the low computational load of the presented approach enables robustness properties, and results very appealing for online use.

Journal ArticleDOI
TL;DR: Simulation and numerical results further illustrate the efficacy and advantages of the proposed CTZD and DTZD models for RTVNO.
Abstract: Online solution of time-varying nonlinear optimization problems is considered an important issue in the fields of scientific and engineering research. In this study, the continuous-time derivative (CTD) model and two gradient dynamics (GD) models are developed for real-time varying nonlinear optimization (RTVNO). A continuous-time Zhang dynamics (CTZD) model is then generalized and investigated for RTVNO to remedy the weaknesses of CTD and GD models. For possible digital hardware realization, a discrete-time Zhang dynamics (DTZD) model, which can be further reduced to Newton-Raphson iteration (NRI), is also proposed and developed. Theoretical analyses indicate that the residual error of the CTZD model has an exponential convergence, and that the maximum steady-state residual error (MSSRE) of the DTZD model has an O(ź2) pattern with ź denoting the sampling gap. Simulation and numerical results further illustrate the efficacy and advantages of the proposed CTZD and DTZD models for RTVNO.

Journal ArticleDOI
TL;DR: In this paper, the restoration problem is transformed into a mixed integer second-order cone programming problem, which can be solved efficiently using several commercial solvers based on the efficient optimization technique family branch and bound.
Abstract: This paper presents a comprehensive mathematical model to solve the restoration problem in balanced radial distribution systems. The restoration problem, originally modeled as mixed integer nonlinear programming, is transformed into a mixed integer second-order cone programming problem, which can be solved efficiently using several commercial solvers based on the efficient optimization technique family branch and bound. The proposed mathematical model considers several objectives in a single objective function, using parameters to preserve the hierarchy of the different objectives: 1) maximizing the satisfaction of the demand, 2) minimizing the number of switch operations, 3) prioritizing the automatic switch operation rather than a manual one, and 4) prioritizing especial loads. General and specialized tests were carried out on a 53-node test system, and the results were compared with other previously proposed algorithms. Results show that the mathematical model is robust, efficient, flexible, and presents excellent performance in finding optimal solutions.

26 Feb 2016
TL;DR: This paper highlights the new features of version 3.2 of the SCIP Optimization Suite and presents new and improved extensions of SCIP, namely solvers for multi-criteria optimization, Steiner tree problems, and mixed-integer semidefinite programs.
Abstract: The SCIP Optimization Suite is a software toolbox for generating and solving various classes of mathematical optimization problems. Its major components are the modeling language ZIMPL, the linear programming solver SoPlex, the constraint integer programming framework and mixed-integer linear and nonlinear programming solver SCIP, the UG framework for parallelization of branch-and-bound-based solvers, and the generic branch-cut-and-price solver GCG. It has been used in many applications from both academia and industry and is one of the leading non-commercial solvers. This paper highlights the new features of version 3.2 of the SCIP Optimization Suite. Version 3.2 was released in July 2015. This release comes with new presolving steps, primal heuristics, and branching rules within SCIP. In addition, version 3.2 includes a reoptimization feature and improved handling of quadratic constraints and special ordered sets. SoPlex can now solve LPs exactly over the rational number and performance improvements have been achieved by exploiting sparsity in more situations. UG has been tested successfully on 80,000 cores. A major new feature of UG is the functionality to parallelize a customized SCIP solver. GCG has been enhanced with a new separator, new primal heuristics, and improved column management. Finally, new and improved extensions of SCIP are presented, namely solvers for multi-criteria optimization, Steiner tree problems, and mixed-integer semidefinite programs.

Journal ArticleDOI
TL;DR: The estimation of superpositions of point sources is studied, which may be used to represent celestial bodies in astronomy, neuron spikes in neuroscience or line spectra in signal processing and spectroscopy.
Abstract: Recent work has shown that convex programming allows to recover a superposition of point sources exactly from low-resolution data as long as the sources are separated by 2/fc, where fc is the cut-off frequency of the sensing process. The proof relies on the construction of a certificate whose existence implies exact recovery. This certificate has since been used to establish that the approach is robust to noise and to analyze related problems such as compressed sensing off the grid and the super-resolution of splines from moment measurements. In this work we construct a new certificate that allows to extend all these results to signals with minimum separations above 1.26/fc. This is close to 1/fc, the threshold at which the problem becomes inherently ill posed, in the sense that signals with a smaller minimum separation may have low-pass projections with negligible energy.

Journal ArticleDOI
TL;DR: The proposed procedure determines the status of the switching devices in order to effectively isolate a faulty zone and minimize the number of de-energized nodes and zones, while ensuring that the operative and electrical constraints of the system are not violated.
Abstract: In this paper, a two-stage procedure is proposed in order to solve the centralized self-healing scheme for electrical distribution systems. The considered self-healing actions are the reconfiguration of the distribution grid and, if needed, node and zone load-shedding. Thus, the proposed procedure determines the status of the switching devices in order to effectively isolate a faulty zone and minimize the number of de-energized nodes and zones, while ensuring that the operative and electrical constraints of the system are not violated. The proposed method is comprised of two stages. The first stage solves a mixed integer linear programming (MILP) problem in order to obtain the binary decision variables for the self-healing scheme (i.e., the switching device status and energized zones). In the second stage, a nonlinear programming (NLP) problem is solved in order to adjust the steady-state operating point of the topology found in the first stage (i.e., correction of the continuous electrical variables and load-shedding optimization). Commercial optimization solvers are used in the first stage to solve the MILP problem and in the second stage to solve the NLP problem. A 44-node test system and a real Brazilian distribution system with 964-nodes were used to test and verify the proposed methodology.

Journal ArticleDOI
TL;DR: A novel algorithm combining the capabilities of chaotic maps and the golden section search method in order to solve nonlinear optimization problems and performs effectively for the engineering applications such as the gear train deign problem.

Journal ArticleDOI
11 Nov 2016
TL;DR: A new gradient descent method using Jacobi preconditioning and Chebyshev acceleration is proposed, comparable to that of L-BFGS or nonlinear conjugate gradient, but unlike other methods, it requires no dot product operation, making it suitable for GPU implementation.
Abstract: We show that many existing elastic body simulation approaches can be interpreted as descent methods, under a nonlinear optimization framework derived from implicit time integration. The key question is how to find an effective descent direction with a low computational cost. Based on this concept, we propose a new gradient descent method using Jacobi preconditioning and Chebyshev acceleration. The convergence rate of this method is comparable to that of L-BFGS or nonlinear conjugate gradient. But unlike other methods, it requires no dot product operation, making it suitable for GPU implementation. To further improve its convergence and performance, we develop a series of step length adjustment, initialization, and invertible model conversion techniques, all of which are compatible with GPU acceleration. Our experiment shows that the resulting simulator is simple, fast, scalable, memory-efficient, and robust against very large time steps and deformations. It can correctly simulate the deformation behaviors of many elastic materials, as long as their energy functions are second-order differentiable and their Hessian matrices can be quickly evaluated. For additional speedups, the method can also serve as a complement to other techniques, such as multi-grid.

Journal ArticleDOI
TL;DR: The results show that the BBO algorithm minimized the benchmark functions accurately, and outperformed the GA in this respect, and reached a near-optimal solution in the case of the single-reservoir hydropower optimization problem.
Abstract: The optimal operation of reservoir systems to meet water demand is a complex and nonlinear problem. This paper applies the biogeography-based optimization (BBO) algorithm to solve reservoir operation problems. The BBO algorithm is first verified with the minimization of three mathematical benchmark functions (Sphere, Rosenbrock, and Bukin6). In addition, the BBO algorithm was applied to a single reservoir system and a four-reservoir system. The performance of the BBO algorithm was compared with that of the genetic algorithm (GA) in solving the three optimization problems. The results show that the BBO algorithm minimized the benchmark functions accurately, and outperformed the GA in this respect. In the case of the single-reservoir hydropower optimization problem the BBO reached a near-optimal solution. The values of the objective function averaged 1.228 and 1.746 with the BBO and GA, respectively. The global solution of this problem with the nonlinear programming method equals 1.213. In the four-...

Journal ArticleDOI
TL;DR: In this paper, a linear approximated methodology for full alternating current-optimal power flow (AC-OPF) is presented, which can provide more precise and real picture of full active and reactive power flow modelling, along with the voltage profile of buses compared to the commonly used direct current-optimality power flow.
Abstract: This study presents a novel linear approximated methodology for full alternating current-optimal power flow (AC-OPF). The AC-OPF can provide more precise and real picture of full active and reactive power flow modelling, along with the voltage profile of buses compared to the commonly used direct current-optimal power flow. While the AC-OPF is a non-linear programming problem, this can be transformed into a mixed-integer linear programming environment by the proposed model without loss of accuracy. The global optimality of the solution for the approximated model can be guaranteed by existing algorithms and software. The numerical results and simulations which represent the effectiveness and applicability of the proposed model are given and completely discussed in this study.