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.

Design Potential Method for Robust System Parameter Design

Abstract: A novel design potential method that integrates the probabilistic constraint evaluation closely into the design optimization process is presented for robust system parameter design. From a broader perspective, it is shown that the probabilistic constraints can be evaluated using either the conventional reliability index approach or the proposed performance measure approach. The performance measure approach is inherently robust and is more effective when the prohahilistic constraint is inactive. The reliability index approach is more effective for the violated probabilistic constraint, but it could yield singularity when the probabilistic constraint is inactive. Moreover, the close coupling of performance probability analysis and design optimization is illustrated in a proposed unified system space. The design potential method, which is developed to take full advantage of the important design information obtained from the previous probabilistic constraint evaluation, can significantly accelerate the convergence of the reliability-based design optimization process.

Optimal design of measures to correct seawater intrusion

Abstract: [1] Numerous studies have been devoted to the optimization of groundwater management strategies in coastal aquifers. However, little has been done to address the problem of initially contaminated aquifers, the subject of this paper. Corrective measures need to be optimally designed to improve water quality while minimizing changes in the existing pumping regime. To this end, we compare two optimization methods. The first one is linear and consists of maximizing pumping rates while constraining heads to prevent seawater inflow. The second one consists of minimizing the changes from current pumping rates, so as to preserve existing rights, while constraining concentrations, which leads to a nonlinear programming problem. In both cases, corrective measures include a reduction in pumping rates, inland artificial recharge, and a coastal hydraulic barrier. Not surprisingly, the nonlinear problem leads to a more efficient solution, both in terms of pumping rates and actual cleanup of the aquifer. Nevertheless, the linear formulation yields insights into the optimal allocation of pumping. More importantly, the linear formulation enables us to readily calculate the hydraulic efficiency (gain in pumping rate per unit increase in recharge rate) of corrective measures. The fact that efficiency is consistently greater than 1 proves that the hydraulic barrier not only increases resources but also protects the existing ones. Therefore we conclude that both optimization approaches are useful and should be used.

Pattern search algorithms for mixed variable general constrained optimization problems

Abstract: : A new class of algorithms for solving nonlinearly constrained mixed variable optimization problems is presented The Audet-Dennis Generalized Pattern Search (GPS) algorithm for bound constrained mixed variable optimization problems is extended to problems with general nonlinear constraints by incorporating a filter in which new iterates are accepted whenever they decrease the incumbent objective function value or constraint violation function value Additionally, the algorithm can exploit any available derivative information (or rough approximation thereof) to speed convergence without sacrificing the flexibility often employed by GPS methods to find better local optima. In generalizing existing GPS algorithms, the new theoretical convergence results presented here reduce seamlessly to existing results for more specific classes of problems. While no local continuity or smoothness assumptions are made, a hierarchy of theoretical convergence results is given, in which the assumptions dictate what can be proved about certain limit points of the algorithm. A new Matlab software package was developed to implement these algorithms. Numerical results are provided for several nonlinear optimization problems from the CUTE test set.

Energy-Efficient Resource Allocation for OFDM-Based Cognitive Radio Networks

Abstract: In this paper, we investigate the energy-efficient resource allocation in orthogonal frequency division multiplexing (OFDM)-based cognitive radio (CR) networks, where we try to maximize the system energy-efficiency under the consideration of many practical limitations, such as transmission power budget of the CR system, interference threshold of primary users and traffic demands of secondary users. Our general objective formulation leads to a challenging mixed integer programming problem that is hard to solve. To make it computationally tractable, we employ a time-sharing method to transform it into a non-linear fractional programming problem, which can be further converted into an equivalent convex optimization problem by using its hypogragh form. Based on these transformations, it is possible to obtain (near) optimal solution by standard optimization technique. However, the complexity of the standard technique is too high for this real-time optimization task. By exploiting the structure of the problem extensively, we develop an efficient barrier method to work out the (near) optimal solution with a reasonable complexity, significantly better than the standard technique. Numerical results show that our proposal can maximize the energy efficiency of the CR system, whilst the proposed algorithm performs quickly and stably.

A Nonlinear Optimization Procedure for Generalized Gaussian Quadratures

Abstract: We present a new nonlinear optimization procedure for the computation of generalized Gaussian quadratures for a broad class of square integrable functions on intervals. While some of the components of this algorithm have been previously published, we present a simple and robust scheme for the determination of a sparse solution to an underdetermined nonlinear optimization problem which replaces the continuation scheme of the previously published works. The new algorithm successfully computes generalized Gaussian quadratures in a number of instances in which the previous algorithms fail. Four applications of our scheme to computational physics are presented: the construction of discrete plane wave expansions for the Helmholtz Green's function, the design of linear array antennae, the computation of a quadrature for the discretization of Laplace boundary integral equations on certain domains with corners, and the construction of quadratures for the discretization of Laplace and Helmholtz boundary integral equations on smooth surfaces.