English

运筹学学报 >

2015 , Vol. 19 >Issue 2: 83 - 90

DOI: https://doi.org/10.15960/j.cnki.issn.1007-6093.2015.02.009

运筹学

双值约束非凸三次规化问题的全局最优性条件

展开
  • 1. 重庆师范大学, 重庆 401331

收稿日期: 2014-03-13

  网络出版日期: 2015-06-15

基金资助

1.国家自然科学基金(Nos. 11471062, 11401064);
2.重庆市自然科学基金(No. cstc2013jcyjA-00021)

收起

Global optimality conditions for non-convex cubic minimization problem with binary constraints

Expand
  • 1. Chongqing Normal University, Chongqing 401331, China

Received date: 2014-03-13

  Online published: 2015-06-15

Fold

摘要

考虑一类带有双值约束的非凸三次优化问题, 给出了该问题的一个全局最优充分必要条件. 结果改进并推广了一些文献中所给出的全局最优性条件, 同时还通过数值例子来说明所给出的全局最优充要条件是易验证的.

关键词： 三次极小化问题; 全局最优性条件; 双值约束

本文引用格式

张亮,王燕,李国权 . 双值约束非凸三次规化问题的全局最优性条件[J]. 运筹学学报, 2015 , 19(2) : 83 -90 . DOI: 10.15960/j.cnki.issn.1007-6093.2015.02.009

Abstract

In this paper, we consider a special non-convex cubic optimization problem with binary constraints, and present a global optimal necessary and sufficient condition for this special non-convex cubic optimization problem. The results of this paper extend some corresponding results on global optimality conditions in some references in present information. Numerical examples show that the global optimal necessary and sufficient condition can effectively determine the optimal solution for the non-convex cubic optimization problem.

Key words： cubic minimization problem; global optimality conditions; binary constraints

参考文献

Beck A, Teboulle M. Global optimality conditions for quadratic optimization problems with binary constraints [J]. SIAM Journal on Optimization, 2000, 11(1): 179-188.
Rubinov A M, Wu Z Y. Optimality conditions in global optimization and their applications [J]. Mathematical Programming, 2009, 120(1): 101-123.
Wu Z Y, Rubinov A M. Global optimality conditions for some classes of optimization problems [J]. Journal of Optimization Theory and Applications, 2010, 145(1): 164-185.
Jeyakumar V, Rubinov A M, Wu Z Y. Sufficient global optimality conditions for non-convex quadratic minimization problems with box constraints [J]. Journal of Global Optimization, 2006, 36(3): 471-481.
Jeyakumar V, Rubinov A M, Wu Z Y. Non-convex quadratic minimization problems with quadratic constraints: global optimality conditions [J]. Mathematical Programming, 2007, 110(3): 521-541.
Zhang X M, Wang Y J, Ma W M. Global sufficient optimality conditions for a special cubic minimization problem [J]. Mathematical Problems in Engineering, 2012, 2012: 1-16.
Wu Z Y, Bai F S. Global optimality conditions for mixed non-convex quadratic programs [J]. Optimization, 2009, 58(1): 39-47.
Hiriart-Urruty J B. Global optimality conditions in maximizing a convex quadratic function under convex quadratic constraints [J]. Journal of Global Optimization, 2001, 21(4): 445-455.
Hiriart-Urruty J B. Conditions for global optimality 2 [J]. Journal of Global Optimization, 1998, 13(4): 349-367.
Strekalovsky A. Global optimality conditions for non-convex optimization [J]. Journal of Global Optimization, 1998, 12(4): 415-434.
Wu Z Y, Jeyakumar V, Rubinov A M. Sufficient conditions for global optimality of bivalent non-convex quadratic programs with inequality constraints [J]. Journal of Optimization Theory and Applications, 2007, 133(1): 123-130.
Chen W, Zhang L S. Global optimality conditions for quadratic 0-1 optimization problems [J]. Journal of Global Optimization, 2010, 46(2): 191-206.
Wu Z Y, Yang Y J, Bai F S, et al. Global optimality conditions and optimization methods for quadratic assignment problems [J]. Applied Mathematics and Computation, 2012, 218(11): 6214-6231.
Wu Z Y, Quan J, Li G Q, et~al. Necessary optimality conditions and new optimization methods for cubic polynomial programming problems with mixed variables [J]. Journal of Optimization Theory and Applications, 2012, 153(2): 408-435.
Wu Z Y, Quan J, Li G Q. Global optimality conditions for some classed of polynomial integer programming problems [J]. Industry and Management Optimization, 2011, 7(1): 67-78.
Tian J, Wu Z Y, Ugon J. Optimization methods for a class of integer polynomial programming problems [J]. Operations Research Transactions, 2011, 15(4): 23-35.
Wang Y J, Liang Z A. Global optimality conditions for cubic minimization problem with box or binary constraints [J]. Journal of Global Optimization, 2010, 47(4): 583-595.
Pardalos P M, Vavasis S A. Quadratic programming with one negative eigenvalue is NP-hard [J]. Journal of Global Optimization, 1991, 1(1): 15-22.
Garey M R, Johnson D S. Computers and Intractability: A Guide to The Theory of NP-Completeness [M]. New York: Freeman, 1979.
Floudas C A, Visweswaran V. Quadratic optimization [J]. Handbook of Global Optimization, 1995, 2: 217-269.
Nie J, Wang L. Regularization methods for SDP relaxations in large-scale polynomial optimization [J]. SIAM Journal on Optimization, 2012, 22(2): 408-428.
Options
文章导航

/

〈 〉