Journal ArticleDOI
Global Optimization of Nonconvex Polynomial Programming Problems HavingRational Exponents
TLDR
An extension of the Reformulation-Linearization Technique (RLT) is developed to generate linear programming relaxations that are embedded within a branch-and-bound algorithm for nonconvex polynomial programming problems that arise in various engineering design, network distribution, and location-allocation contexts.Abstract:
This paper considers the solution of nonconvex polynomial programming problems that arise in various engineering design, network distribution, and location-allocation contexts. These problems generally have nonconvex polynomial objective functions and constraints, involving terms of mixed-sign coefficients (as in signomial geometric programs) that have rational exponents on variables. For such problems, we develop an extension of the Reformulation-Linearization Technique (RLT) to generate linear programming relaxations that are embedded within a branch-and-bound algorithm. Suitable branching or partitioning strategies are designed for which convergence to a global optimal solution is established. The procedure is illustrated using a numerical example, and several possible extensions and algorithmic enhancements are discussed.read more
Citations
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Journal ArticleDOI
A tutorial on geometric programming
TL;DR: This tutorial paper collects together in one place the basic background material needed to do GP modeling, and shows how to recognize functions and problems compatible with GP, and how to approximate functions or data in a formcompatible with GP.
Journal ArticleDOI
A review of recent advances in global optimization
TL;DR: This paper presents an overview of the research progress in deterministic global optimization during the last decade (1998-2008).
Book
Monotonic Optimization in Communication and Networking Systems
TL;DR: This monograph provides a succinct and accessible introduction to monotonic optimization, including the formulation skills and solution algorithms, and aims to spur new research activities in broadening the scope of application of monotony optimization in communication and networking systems.
Book ChapterDOI
Reformulations in Mathematical Programming: A Computational Approach
TL;DR: A survey of existing reformulations interpreted along these lines, some example applications, and the implementation of a software framework for reformulation and optimization are presented.
Journal ArticleDOI
Global optimization of nonconvex factorable programming problems
Hanif D. Sherali,Hongjie Wang +1 more
TL;DR: A branch-and-bound approach based on linear programming relaxations generated through various approximation schemes that utilize, for example, the Mean-Value Theorem and Chebyshev interpolation polynomials coordinated with a Reformulation-Linearization Technique (RLT).
References
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Book
Global Optimization: Deterministic Approaches
Reiner Horst,Tuy Hoang +1 more
TL;DR: This study develops a unifying approach to constrained global optimization that provides insight into the underlying concepts and properties of diverse techniques recently proposed to solve a wide variety of problems encountered in the decision sciences, engineering, operations research and other disciplines.
Journal ArticleDOI
Jointly Constrained Biconvex Programming
Faiz A. Al-Khayyal,James E. Falk +1 more
TL;DR: It is proved that the minimum of a biconcave function over a nonempty compact set occurs at a boundary point of the set and not necessarily an extreme point and the algorithm is proven to converge to a global solution of the nonconvex program.
Book
A Collection of Test Problems for Constrained Global Optimization Algorithms
TL;DR: Quadratic programming test problems, quadratically constrained test problems and nonlinear program test problems have been reported in this article, including the following problems: quadratic programming, nonlinear programming, pooling/blending, and chemical reaction equilibrium test problems.
Journal ArticleDOI
Algorithm 652: HOMPACK: a suite of codes for globally convergent homotopy algorithms
TL;DR: HOMPACK provides three qualitatively different algorithms for tracking the homotopy zero curve: ordinary differential equation-based, normal flow, and augmented Jacobian matrix.