|本期目录/Table of Contents|

[1]章显业,罗和治.带凸二次约束非凸二次规划的双非负规划松弛及其解法[J].浙江理工大学学报,2022,47-48(自科四):601-607.
　ZHANG Xianye,LUO Hezhi.Doubly non negative programming relaxation for non convex quadratic programming with convex quadratic constraint and its solution[J].Journal of Zhejiang Sci-Tech University,2022,47-48(自科四):601-607.
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带凸二次约束非凸二次规划的双非负规划松弛及其解法()
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浙江理工大学学报[ISSN:1673-3851/CN:33-1338/TS]

卷:
第47-48卷
期数:
2022年自科第四期
页码:
601-607
栏目:
出版日期:
2022-09-30

文章信息/Info

Title:
Doubly non negative programming relaxation for non convex quadratic programming with convex quadratic constraint and its solution
文章编号:
1673-3851 (2022) 07-0601-07
作者:
章显业; 罗和治
浙江理工大学理学院，杭州 310018
Author(s):
ZHANG Xianye; LUO Hezhi
chool of Science, Zhejiang Sci-Tech University, Hangzhou 310018, China
关键词:
非凸二次规划; 双非负规划松弛; 交替方乘子向法; 半定规划; CVX
分类号:
O221
文献标志码:
A
摘要:
针对带有非负变量、线性等式和凸二次约束的非凸二次规划问题，给出了一个带有矩阵非负和半正定约束的紧双非负规划(Doubly nonnegative programming, DNP)松弛，估计了它与原问题之间的间隙，并提出了求DNP松弛最优解的交替方向乘子法。数值实验表明：交替方向乘子法能有效找到DNP松弛问题的最优解，并且计算时间优于求解器CVX。

参考文献/References:

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［2］Pardalos P M, Schnitger G. Checking local optimality in constrained quadratic programming is NPhard［J］. Operations Research Letters, 1988, 7(1): 33-35.

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［5］Le Thi H A, Dinh T P. A branch and bound method via d.c. optimization algorithms and ellipsoidal technique for box constrained nonconvex quadratic problems［J］. Journal of Global Optimization, 1998, 13: 171-206.

［6］Hoai An L T. An efficient algorithm for globally minimizing a quadratic function under convex quadratic constraints［J］. Mathematical Programming, 2000, 87(3): 401-426.

［7］Barrientos O, Correa R. An algorithm for global minimization of linearly constrained quadratic functions［J］. J Global Optimization, 2000, 16(1): 77-93.

［8］Burer S, Vandenbussche D. A finite branchandbound algorithm for nonconvex quadratic programming via semidefinite relaxations［J］. Mathematical Programming, 2008, 113(2): 259-282.

［9］Luo H Z, Bai X D, Lim G, et al. New global algorithms for quadratic programming with a few negative eigenvalues based on alternative direction method and convex relaxation［J］. Mathematical Programming Computation, 2019, 11(1): 119-171.

［10］Anstreicher K M. Semidefinite programming versus the reformulationlinearization technique for nonconvex quadratically constrained quadratic programming［J］. Journal of Global Optimization, 2009, 43(2/3): 471-484.

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备注/Memo

备注/Memo:
收稿日期： 2022-02-16
网络出版日期：2022-04-06
基金项目： 浙江省自然科学基金重点项目(LZ21A010003)；国家自然科学基金项目（11871433）
作者简介： 章显业(1997-)，男，浙江温州人，硕士研究生，主要从事最优化理论与算法方面的研究
通信作者： 罗和治，E-mail：hzluo@zstu.edu.cn
更新日期/Last Update: 2022-09-06