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.

Scatter Search and Local NLP Solvers: A Multistart Framework for Global Optimization

Abstract: The algorithm described here, called OptQuest/NLP or OQNLP, is a heuristic designed to find global optima for pure and mixed integer nonlinear problems with many constraints and variables, where all problem functions are differentiable with respect to the continuous variables. It uses OptQuest, a commercial implementation of scatter search developed by OptTek Systems, Inc., to provide starting points for any gradient-based local solver for nonlinear programming (NLP) problems. This solver seeks a local solution from a subset of these points, holding discrete variables fixed. The procedure is motivated by our desire to combine the superior accuracy and feasibility-seeking behavior of gradient-based local NLP solvers with the global optimization abilities of OptQuest. Computational results include 155 smooth NLP and mixed integer nonlinear program (MINLP) problems due to Floudas et al. (1999), most with both linear and nonlinear constraints, coded in the GAMS modeling language. Some are quite large for global optimization, with over 100 variables and 100 constraints. Global solutions to almost all problems are found in a small number of local solver calls, often one or two.

Handbook of applied optimization

Abstract: PrefacePanos M. Pardalos and Mauricio G. C. Resende: IntroductionPanos M. Pardalos and Mauricio G. C. Resende: Part One: Algorithms 1: Linear Programming 1.1: Tamas Terlaky: Introduction 1.2: Tamas Terlaky: Simplex-Type Algorithms 1.3: Kees Roos: Interior-Point Methods for Linear Optimization 2: Henry Wolkowicz: Semidefinite Programming 3: Combinatorial Optimization 3.1: Panos M. Pardalos and Mauricio G. C. Resende: Introduction 3.2: Eva K. Lee: Branch-and-Bound Methods 3.3: John E. Mitchell: Branch-and-Cut Algorithms for Combinatorial Optimization Problems 3.4: Augustine O. Esogbue: Dynamic Programming Approaches 3.5: Mutsunori Yagiura and Toshihide Ibaraki: Local Search 3.6: Metaheuristics 3.6.1: Bruce L. Golden and Edward A. Wasil: Introduction 3.6.2: Eric D. Taillard: Ant Systems 3.6.3: John E. Beasley: Population Heuristics 3.6.4: Pablo Moscato: Memetic Algorithms 3.6.5: Leonidas S. Pitsoulis and Mauricio G. C. Resende: Greedy Randomized Adaptive Search Procedures 3.6.6: Manuel Laguna: Scatter Search 3.6.7: Fred Glover and Manuel Laguna: Tabu Search 3.6.8: E. H. L. Aarts and H. M. M. Ten Eikelder: Simulated Annealing 3.6.9: Pierre Hansen and Nenad Mladenovi'c: Variable Neighborhood Search 4: Yinyu Ye: Quadratic Programming 5: Nonlinear Programming 5.1: Gianni Di Pillo and Laura Palagi: Introduction 5.2: Gianni Di Pillo and Laura Palagi: Unconstrained Nonlinear Programming 5.3: Constrained Nonlinear Programming }a Gianni Di Pillo and Laura Palagi 5.4: Manlio Gaudioso: Nonsmooth Optimization 6: Christodoulos A. Floudas: Deterministic Global Optimizatio and Its Applications 7: Philippe Mahey: Decomposition Methods for Mathematical Programming 8: Network Optimization 8.1: Ravindra K. Ahuja, Thomas L. Magnanti, and James B. Orlin: Introduction 8.2: Ravindra K. Ahuja, Thomas L. Magnanti, and James B. Orlin: Maximum Flow Problem 8.3: Edith Cohen: Shortest-Path Algorithms 8.4: S. Thomas McCormick: Minimum-Cost Single-Commodity Flow 8.5: Pierre Chardaire and Abdel Lisser: Minimum-Cost Multicommodity Flow 8.6: Ravindra K. Ahuja, Thomas L. Magnanti, and James B. Orlin: Minimum Spanning Tree Problem 9: Integer Programming 9.1: Nelson Maculan: Introduction 9.2: Nelson Maculan: Linear 0-1 Programming 9.3: Yves Crama and peter L. Hammer: Psedo-Boolean Optimization 9.4: Christodoulos A. Floudas: Mixed-Integer Nonlinear Optimization 9.5: Monique Guignard: Lagrangian Relaxation 9.6: Arne Lookketangen: Heuristics for 0-1 Mixed-Integer Programming 10: Theodore B. Trafalis and Suat Kasap: Artificial Neural Networks in Optimization and Applications 11: John R. Birge: Stochastic Programming 12: Hoang Tuy: Hierarchical Optimization 13: Michael C. Ferris and Christian Kanzow: Complementarity and Related Problems 14: Jose H. Dula: Data Envelopment Analysis 15: Yair Censor and Stavros A. Zenios: Parallel Algorithms in Optimization 16: Sanguthevar Rajasekaran: Randomization in Discrete Optimization: Annealing Algorithms Part Two: Applications 17: Problem Types 17.1: Chung-Yee Lee and Michael Pinedo: Optimization and Heuristics of Scheduling 17.2: John E. Beasley, Abilio Lucena, and Marcus Poggi de Aragao: The Vehicle Routing Problem 17.3: Ding-Zhu Du: Network Designs: Approximations for Steiner Minimum Trees 17.4: Edward G. Coffman, Jr., Janos Csirik, and Gerhard J. Woeginger: Approximate Solutions to Bin Packing Problems 17.5: Rainer E. Burkard: The Traveling Salesmand Problem 17.6: Dukwon Kim and Boghos D. Sivazlian: Inventory Management 17.7: Zvi Drezner: Location 17.8: Jun Gu, Paul W. Purdom, John Franco, and Benjamin W. Wah: Algorithms for the Satisfiability (SAT) Problem 17.9: Eranda Cela: Assignment Problems 18: Application Areas 18.1: Warren B. Powell: Transportation and Logistics 18.2: Gang Yu and Benjamin G. Thengvall: Airline Optimization 18.3: Alexandra M. Newman, Linda K. Nozick, and Candace Arai Yano: Optimization in the Rail Industry 18.4: Andres Weintraub Pohorille and John Hof: Forstry Industry 18.5: Stephen C. Graves: Manufacturing Planning and Control 18.6: Robert C. Leachman: Semiconductor Production Planning 18.7: Matthew E. Berge, John T. Betts, Sharon K. Filipowski, William P. Huffman, and David P. Young: Optimization in the Aerospace Industry 18.8: Energy 18.8.1: Gerson Couto de Oliveira, Sergio Granville, and Mario Pereira: Optimization in Electrical Power Systems 18.8.2: Roland N. Horne: Optimization Applications in Oil and Gas Recovery 18.8.3: Roger Z. Rios-Mercado: Natural Gas Pipeline Optimization 18.9: G. Anandalingam: Opimization of Telecommunications Networks 18.10: Stanislav Uryasev: Optimization of Test Intervals in Nuclear Engineering 18.11: Hussein A. Y. Etawil and Anthony Vannelli: Optimization in VLSI Design: Target Distance Models for Cell Placement 18.12: Michael Florian and Donald W. Hearn: Optimization Models in Transportation Planning 18.13: Guoliang Xue: Optimization in computation Molecular Biology 18.14: Anna Nagurney: Optimization in the Financial Services Industry 18.15: J. B. Rosen, John H. Glick, and E. Michael Gertz: Applied Large-Scale Nonlinear Optimization for Optimal Control of Partial Differential Equations and Differential Algebraic Equations 18.16: Kumaraswamy Ponnambalam: Optimization in Water Reservoir Systems 18.17: Ivan Dimov and Zahari Zlatev: Optimization Problems in Air-Pollution Modeling 18.18: Charles B. Moss: Applied Optimization in Agriculture 18.19: Petra Mutzel: Optimization in Graph Drawing 18.20: G. E. Stavroulakis: Optimization for Modeling of Nonlinear Interactions in Mechanics Part Three: Software 19: Emmanuel Fragniere and Jacek Gondzio: Optimization Modeling Languages 20: Stephen J. Wright: Optimization Software Packages 21: Andreas Fink, Stefan VoB, and David L. Woodruff: Optimization Software Libraries 22: John E. Beasley: Optimization Test Problem Libraries 23: Simone de L. Martins, Celso C. Ribeiro, and Noemi Rodriguez: Parallel Computing Environment 24: Catherine C. McGeoch: Experimental Analysis of Optimization Algorithms 25: Andreas Fink, Stefan VoB, and David L. Woodruff: Object-Oriented Programming 26: Michael A. Trick: Optimization and the Internet Directory of Contributors Index

Convex Programming with Set-Inclusive Constraints and Applications to Inexact Linear Programming

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

Review of Nonlinear Mixed-Integer and Disjunctive Programming Techniques

Abstract: This paper has as a major objective to present a unified overview and derivation of mixed-integer nonlinear programming (MINLP) techniques, Branch and Bound, Outer-Approximation, Generalized Benders and Extended Cutting Plane methods, as applied to nonlinear discrete optimization problems that are expressed in algebraic form. The solution of MINLP problems with convex functions is presented first, followed by a brief discussion on extensions for the nonconvex case. The solution of logic based representations, known as generalized disjunctive programs, is also described. Theoretical properties are presented, and numerical comparisons on a small process network problem.