Nonlinear programming

About: Nonlinear programming is a research topic. Over the lifetime, 19486 publications have been published within this topic receiving 656602 citations. The topic is also known as: non-linear programming & NLP.

MEIGO: an open-source software suite based on metaheuristics for global optimization in systems biology and bioinformatics

Abstract: Optimization is the key to solving many problems in computational biology. Global optimization methods, which provide a robust methodology, and metaheuristics in particular have proven to be the most efficient methods for many applications. Despite their utility, there is a limited availability of metaheuristic tools. We present MEIGO, an R and Matlab optimization toolbox (also available in Python via a wrapper of the R version), that implements metaheuristics capable of solving diverse problems arising in systems biology and bioinformatics. The toolbox includes the enhanced scatter search method (eSS) for continuous nonlinear programming (cNLP) and mixed-integer programming (MINLP) problems, and variable neighborhood search (VNS) for Integer Programming (IP) problems. Additionally, the R version includes BayesFit for parameter estimation by Bayesian inference. The eSS and VNS methods can be run on a single-thread or in parallel using a cooperative strategy. The code is supplied under GPLv3 and is available at http://www.iim.csic.es/~gingproc/meigo.html . Documentation and examples are included. The R package has been submitted to BioConductor. We evaluate MEIGO against optimization benchmarks, and illustrate its applicability to a series of case studies in bioinformatics and systems biology where it outperforms other state-of-the-art methods. MEIGO provides a free, open-source platform for optimization that can be applied to multiple domains of systems biology and bioinformatics. It includes efficient state of the art metaheuristics, and its open and modular structure allows the addition of further methods.

Path-constrained trajectory optimization using sparse sequential quadratic programming

Abstract: One of the most effective numerical techniques for the solution of trajectory optimization and optimal control problems is the direct transcription method. This approach combines a nonlinear programming algorithm with discretization of the trajectory dynamics. The resulting mathematical programming problem is characterized by matrices that are large and sparse. Constraints on the path of the trajectory are then treated as algebraic inequalities to be satisfied by the nonlinear program. This paper describes a nonlinear programming algorithm that exploits the matrix sparsity produced by the transcription formulation. Numerical experience is reported for trajectories with both state and control variable equality and inequality path constraints. T is well known that the solution of an optimal control or trajectory optimization problem can be posed as the solution of a two-point boundary value problem. This problem requires solving a set of nonlinear ordinary differential equations; the first set defined by the vehicle dynamics and the second set (of adjoint differential equations) by the optimality conditions. Boundary conditions are imposed from the problem requirements as well as the optimality criteria. By discretizing the dynamic variables, this boundary value problem can be reduced to the solution of a set of nonlinear algebraic equations. This approach has been successfully utilized1'5 for applications without path constraints. Since the approach requires adjoint equations, it is subject to a number of difficulties. First, the adjoint equations are often very nonlinear and cumbersome to obtain for complex vehicle dynamics, especially when thrust and aerodynamic forces are given by tabular data. Second, the iterative procedure requires an initial guess for the adjoint variables, and this can be quite difficult because they lack a physical interpretation. Third, convergence of the iterations is often quite sensitive to the accuracy of the adjoint guess. Finally, the adjoint variables may be discontinuous when the solution enters or leaves an inequality path constraint. Difficulties associated with adjoint equations are avoided by the direct transcription or collocation methods.6'10 In this approach, the dynamic equations are discretized, and the optimal control problem is transformed into a nonlinear program, which can be solved directly. The nonlinear programming problem is large and sparse and a method for solving it is presented in Ref. 7. This paper extends the method of Ref. 7 to efficiently handle inequality constraints and presents a nonlinear programming algorithm designed to exploit the properties of the problem that results from direct transcription of the trajectory optimization application.

Some Guidelines for Constructing Exact D-Optimal Designs on Convex Design Spaces

Abstract: Some problems unique to the construction of N-point D-optimal designs on convex design spaces are considered. Multiple-point augmentation and exchange algorithms are shown to be more costly and less efficient than the analogous single-point procedures. Moreover, some recommendations for improving single-point methods are given. Finally, empirical evidence is found that supports the Galil and Kiefer option for constructing initial designs and Powell's optimization method for design augmentation.

A screening and optimization approach for the retrofit of heat-exchanger networks

Abstract: On presente une methode systematique pour la readaptation de reseaux d'echangeurs de chaleur