Global optimality conditions and optimization methods for quadratic integer programming problems

Authors:
Z. Y. Wu;G. Q. Li;J. Quan
Affiliations:
School of Information Technology and Mathematical Sciences, University of Ballarat, Ballarat, Australia 3353;Department of Mathematics, Shanghai University, Shanghai, China 200444;Department of Mathematics, Shanghai University, Shanghai, China 200444
Venue:
Journal of Global Optimization
Year:
2011

Citing 15
Cited 0

Computational aspects of a branch and bound algorithm for quadratic zero-one programming

Computing
Improved approximation algorithms for maximum cut and satisfiability problems using semidefinite programming

Journal of the ACM (JACM)
Global Optimization Techniques for Solving the General Quadratic Integer Programming Problem

Computational Optimization and Applications
Outward rotations: a tool for rounding solutions of semidefinite programming relaxations, with applications to MAX CUT and other problems

STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
Computers and Intractability: A Guide to the Theory of NP-Completeness

Computers and Intractability: A Guide to the Theory of NP-Completeness
Rank-Two Relaxation Heuristics for MAX-CUT and Other Binary Quadratic Programs

SIAM Journal on Optimization
Global Optimality Conditions for Quadratic Optimization Problems with Binary Constraints

SIAM Journal on Optimization
A provable better Branch and Bound method for a nonconvex integer quadratic programming problem

Journal of Computer and System Sciences
Lagrangian Smoothing Heuristics for Max-Cut

Journal of Heuristics
Lower Bound Improvement and Forcing Rule for Quadratic Binary Programming

Computational Optimization and Applications
On the gap between the quadratic integer programming problem and its semidefinite relaxation

Mathematical Programming: Series A and B
Non-convex quadratic minimization problems with quadratic constraints: global optimality conditions

Mathematical Programming: Series A and B
New bounds on the unconstrained quadratic integer programming problem

Journal of Global Optimization
Global optimality conditions for quadratic 0-1 optimization problems

Journal of Global Optimization
A max-flow approach to improved lower bounds for quadratic unconstrained binary optimization (QUBO)

Discrete Optimization

Quantified Score

Hi-index	0.00

Visualization

Abstract

In this paper, we first establish some sufficient and some necessary global optimality conditions for quadratic integer programming problems. Then we present a new local optimization method for quadratic integer programming problems according to its necessary global optimality conditions. A new global optimization method is proposed by combining its sufficient global optimality conditions, local optimization method and an auxiliary function. The numerical examples are also presented to show that the proposed optimization methods for quadratic integer programming problems are very efficient and stable.