Global Optimization of Nonconvex Polynomial Programming Problems HavingRational Exponents

Authors:
Hanif D. Sherali
Affiliations:
Department of Industrial and Systems Engineering, Virginia Polytechnic Institute and State University, Blacksburg, VA 24061-0118, U.S.A.
Venue:
Journal of Global Optimization
Year:
1998

Citing 7
Cited 9

A collection of test problems for constrained global optimization algorithms

A collection of test problems for constrained global optimization algorithms
Dual quadratic estimates in polynomial and boolean programming

Annals of Operations Research
Algorithm 652: HOMPACK: a suite of codes for globally convergent homotopy algorithms

ACM Transactions on Mathematical Software (TOMS)
A Global Optimization Approach to a Water Distribution Network DesignProblem

Journal of Global Optimization
Comparison of Two Reformulation-Linearization TechniqueBased Linear Programming Relaxations for Polynomial Programming Problems

Journal of Global Optimization
Solving the pooling problem using generalized reduced gradient and successive linear programming algorithms

ACM SIGMAP Bulletin
New reformulation linearization/convexification relaxations for univariate and multivariate polynomial programming problems

Operations Research Letters

A Pseudo-Global Optimization Approach with Application to the Design of Containerships

Journal of Global Optimization
Optimization of Polynomial Fractional Functions

Journal of Global Optimization
Computing exact solution to nonlinear integer programming: Convergent Lagrangian and objective level cut method

Journal of Global Optimization
Global optimization for sum of generalized fractional functions

Journal of Computational and Applied Mathematics
Global Optimization of Robot Control System Via Generalized Geometric Programming

ICIRA '08 Proceedings of the First International Conference on Intelligent Robotics and Applications: Part I
A review of recent advances in global optimization

Journal of Global Optimization
Global optimization of generalized geometric programming

Computers & Mathematics with Applications
An Efficient Global Approach for Posynomial Geometric Programming Problems

INFORMS Journal on Computing
Efficient pruning technique based on linear relaxations

COCOS'03 Proceedings of the Second international conference on Global Optimization and Constraint Satisfaction

Quantified Score

Hi-index	0.00

Visualization

Abstract

This paper considers the solution of nonconvex polynomial programmingproblems that arise in various engineering design, network distribution, andlocation-allocation contexts. These problems generally have nonconvexpolynomial objective functions and constraints, involving terms ofmixed-sign coefficients (as in signomial geometric programs) that haverational exponents on variables. For such problems, we develop an extensionof the Reformulation-Linearization Technique (RLT) to generate linearprogramming relaxations that are embedded within a branch-and-boundalgorithm. Suitable branching or partitioning strategies are designed forwhich convergence to a global optimal solution is established. The procedureis illustrated using a numerical example, and several possible extensionsand algorithmic enhancements are discussed.