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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.


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TL;DR: The differential-algebraic equation (DAE) optimization problem is transformed to a nonlinear programming problem by applying collocation on finite elements using a reduced space successive quadratic programming (rSQP) algorithm, which solves more than 150 DAEs in less than 7 CPU minutes.
Abstract: The differential-algebraic equation (DAE) optimization problem is transformed to a nonlinear programming problem by applying collocation on finite elements. The resulting problem is solved using a reduced space successive quadratic programming (rSQP) algorithm. Here, the variable space is partitioned into range and null spaces. Partitioning by choosing a pivot sequence for an LU factorization with partial pivoting allows us to detect unstable modes in the DAE system, which can now be stabilized without imposing new boundary conditions. As a result, the range space is decomposed in a single step by exploiting the overall sparsity of the collocation matrix; which performs better than the two-step condensation method used in standard collocation solvers. To deal with ill-conditioned constraints, we also extend the rSQP algorithm to include dogleg steps for the range space step that solves the collocation equations. The performance of this algorithm was tested on two well known unstable problems and on three chemical engineering examples including two reactive distillation columns and a plug-flow reactor with free radicals. One of these is u batch column where an equilibrium reaction takes place. The second reactive distillation problem is the startup of a continuous column with competitive reactions. These optimization problems, which include more than 150 DAEs, ure solved in less than 7 CPU minutes on workstation class computers.

152 citations

Journal ArticleDOI
TL;DR: This paper addresses two second-best toll pricing problems, one with fixed and the other with elastic travel demands, as mathematical programs with equilibrium constraints, and several equivalent nonlinear programming formulations for the two problems are discussed.
Abstract: This paper addresses two second-best toll pricing problems, one with fixed and the other with elastic travel demands, as mathematical programs with equilibrium constraints. Several equivalent nonlinear programming formulations for the two problems are discussed. One formulation leads to properties that are of interest to transportation economists. Another produces an algorithm that is capable of solving large problems and easy to implement with existing software for linear and nonlinear programming problems. Numerical results using transportation networks from the literature are also presented.

152 citations

Journal ArticleDOI
TL;DR: The generalized Lloyd algorithm for vector quantizer design is analyzed as a descent algorithm for nonlinear programming and a well-known convergence theorem is applied to show that iterative applications of the algorithm produce a sequence of quantizers that approaches the set of fixed-point quantizers.
Abstract: The generalized Lloyd algorithm for vector quantizer design is analyzed as a descent algorithm for nonlinear programming. A broad class of convex distortion functions is considered and any input distribution that has no singular-continuous part is allowed. A well-known convergence theorem is applied to show that iterative applications of the algorithm produce a sequence of quantizers that approaches the set of fixed-point quantizers. The methods of the theorem are extended to sequences of algorithms, yielding results on the behavior of the algorithm when an unknown distribution is approximated by a training sequence of observations. It is shown that as the length of the training sequence grows large that 1) fixed-point quantizers for the training sequence approach the set of fixed-point quantizers for the true distribution, and 2) limiting quantizers produced by the algorithm with the training sequence distribution perform no worse than limiting quantizers produced by the algorithm with the true distribution.

152 citations

Journal ArticleDOI
TL;DR: A characterization of strong regularity in terms of second order optimality conditions for nonpolyhedral conic problem is given, the first time such a characterization is given for a nonPolyhedral Conic problem.
Abstract: We discuss first and second order optimality conditions for nonlinear second-order cone programming problems, and their relation with semidefinite programming problems. For doing this we extend in an abstract setting the notion of optimal partition. Then we state a characterization of strong regularity in terms of second order optimality conditions. This is the first time such a characterization is given for a nonpolyhedral conic problem.

152 citations

Journal ArticleDOI
TL;DR: A unified approach to load-flow, minimum-loss, and economic dispatching problems is presented and a unconstrained minimization method is shown to coincide with the minimum of a function of the power system equations.
Abstract: A unified approach to load-flow, minimum-loss, and economic dispatching problems is presented. A load-flow solution is shown to coincide with the minimum of a function of the power system equations. An unconstrained minimization method, developed by Fletcher-Powell, is used to solve the load-flow problem. The method always finds a solution or indicates the nonexistence of a solution. Its performance is highly independent of the reference- slack bus position and requires no acceleration factors. Several constrained minimization techniques that solve the minimum-loss and economic dispatching problems are investigated. These include the Fiacco-McCormick, Lootsma, and Zangwill methods. The technique finally recommended is shown to be an extension of the method used to solve the load-flow problem. The approved IEEE test systems, and other systems whose response to conventional methods was known, have been solved.

151 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
2023113
2022259
2021615
2020650
2019640
2018630