More test examples for nonlinear programming codes
More test examples for nonlinear programming codes
Dual quadratic estimates in polynomial and boolean programming
Annals of Operations Research
SIAM Review
Global Optimization with Polynomials and the Problem of Moments
SIAM Journal on Optimization
An Explicit Equivalent Positive Semidefinite Program for Nonlinear 0-1 Programs
SIAM Journal on Optimization
Enhancing RLT relaxations via a new class of semidefinite cuts
Journal of Global Optimization
Cutting Plane Algorithms for Nonlinear Semi-Definite Programming Problems with Applications
Journal of Global Optimization
Semidefinite Programming vs. LP Relaxations for Polynomial Programming
Mathematics of Operations Research
GloptiPoly: Global optimization over polynomials with Matlab and SeDuMi
ACM Transactions on Mathematical Software (TOMS)
Global optimization of mixed-integer nonlinear programs: A theoretical and computational study
Mathematical Programming: Series A and B
A finite branch-and-bound algorithm for nonconvex quadratic programming via semidefinite relaxations
Mathematical Programming: Series A and B
Computational Optimization and Applications
Strong Duality for the CDT Subproblem: A Necessary and Sufficient Condition
SIAM Journal on Optimization
Reduced RLT representations for nonconvex polynomial programming problems
Journal of Global Optimization
Branch and cut algorithms for detecting critical nodes in undirected graphs
Computational Optimization and Applications
Journal of Global Optimization
Hi-index | 0.00 |
In this paper, we propose to enhance Reformulation-Linearization Technique (RLT)-based linear programming (LP) relaxations for polynomial programming problems by developing cutting plane strategies using concepts derived from semidefinite programming. Given an RLT relaxation, we impose positive semidefiniteness on suitable dyadic variable-product matrices, and correspondingly derive implied semidefinite cuts. In the case of polynomial programs, there are several possible variants for selecting such particular variable-product matrices on which positive semidefiniteness restrictions can be imposed in order to derive implied valid inequalities. This leads to a new class of cutting planes that we call v-semidefinite cuts. We explore various strategies for generating such cuts, and exhibit their relative effectiveness towards tightening the RLT relaxations and solving the underlying polynomial programming problems in conjunction with an RLT-based branch-and-cut scheme, using a test-bed of problems from the literature as well as randomly generated instances. Our results demonstrate that these cutting planes achieve a significant tightening of the lower bound in contrast with using RLT as a stand-alone approach, thereby enabling a more robust algorithm with an appreciable reduction in the overall computational effort, even in comparison with the commercial software BARON and the polynomial programming problem solver GloptiPoly.