Theoretical filtering of RLT bound-factor constraints for solving polynomial programming problems to global optimality

Authors:
Evrim Dalkiran;Hanif D. Sherali
Affiliations:
Department of Industrial and Systems Engineering, Wayne State University, Detroit, USA 48202;Grado Department of Industrial and Systems Engineering, Virginia Tech, Blacksburg, USA 24061
Venue:
Journal of Global Optimization
Year:
2013

Citing 23
Cited 0

Dual quadratic estimates in polynomial and boolean programming

Annals of Operations Research
Test Examples for Nonlinear Programming Codes

Test Examples for Nonlinear Programming Codes
Global Optimization with Polynomials and the Problem of Moments

SIAM Journal on Optimization
A Convex Envelope Formula for Multilinear Functions

Journal of Global Optimization
Enhancing RLT relaxations via a new class of semidefinite cuts

Journal of Global Optimization
A Comparison of the Sherali-Adams, Lovász-Schrijver, and Lasserre Relaxations for 0--1 Programming

Mathematics of Operations Research
Global optimization of mixed-integer nonlinear programs: A theoretical and computational study

Mathematical Programming: Series A and B
SNOPT: An SQP Algorithm for Large-Scale Constrained Optimization

SIAM Review
A polyhedral branch-and-cut approach to global optimization

Mathematical Programming: Series A and B
Linearity Embedded in Nonconvex Programs

Journal of Global Optimization
Studies of the behavior of recursion for the pooling problem

ACM SIGMAP Bulletin
Sums of Squares and Semidefinite Program Relaxations for Polynomial Optimization Problems with Structured Sparsity

SIAM Journal on Optimization
An Exact Reformulation Algorithm for Large Nonconvex NLPs Involving Bilinear Terms

Journal of Global Optimization
Convergent SDP-Relaxations in Polynomial Optimization with Sparsity

SIAM Journal on Optimization
Algorithm 883: SparsePOP---A Sparse Semidefinite Programming Relaxation of Polynomial Optimization Problems

ACM Transactions on Mathematical Software (TOMS)
Semidefinite programming versus the reformulation-linearization technique for nonconvex quadratically constrained quadratic programming

Journal of Global Optimization
Multiterm polyhedral relaxations for nonconvex, quadratically constrained quadratic programs

Optimization Methods & Software - GLOBAL OPTIMIZATION
Constrained global optimization of multivariate polynomials using Bernstein branch and prune algorithm

Journal of Global Optimization
Combined bound-grid-factor constraints for enhancing RLT relaxations for polynomial programs

Journal of Global Optimization
Reduced RLT representations for nonconvex polynomial programming problems

Journal of Global Optimization
New reformulation linearization/convexification relaxations for univariate and multivariate polynomial programming problems

Operations Research Letters
Enhancing RLT-based relaxations for polynomial programming problems via a new class of v-semidefinite cuts

Computational Optimization and Applications
Compact relaxations for polynomial programming problems

SEA'12 Proceedings of the 11th international conference on Experimental Algorithms

Quantified Score

Hi-index	0.00

Visualization

Abstract

In this paper, we propose two sets of theoretically filtered bound-factor constraints for constructing reformulation-linearization technique (RLT)-based linear programming (LP) relaxations for solving polynomial programming problems. We establish related theoretical results for convergence to a global optimum for these reduced sized relaxations, and provide insights into their relative sizes and tightness. Extensive computational results are provided to demonstrate the relative effectiveness of the proposed theoretical filtering strategies in comparison to the standard RLT and a prior heuristic filtering technique using problems from the literature as well as randomly generated test cases.