凸规划的动边界组合同伦方法及其收敛性

Boundary Moving Combined Homotopy Method for Nonconvex Nonlinear Programming and Its Convergence

SHANG Yu-feng¹,², YU Bo³

1. Institute of Mathematics, Jilin University, Changchun 130012, China; 2. Department of Foundation, Aviation University of Air Force, Changchun 130022, China; 3. Department of Applied Mathematics, Dalian University of Technology, Dalian 116024, Liaoning Province, China

Received:2005-10-25 Revised:1900-01-01 Online:2006-05-26 Published:2006-05-26
Contact: SHANG Yu-feng

Abstract

Abstract: A new homotopy method, called boundary moving combined homotopy method, for solving convex programming was presented. Existence and conv ergence of a homotopy path were proved under only Slater’s condition and a coercive condition. In contrast to the existed combined homotopy interior point methods, the start point needs not to be an interior point of the feasible set, so the new method is more convenient to use. Some numerical examples are given to show its efficiency.

Key words: nonlinear programming, convex programming, homotopy method

CLC Number:

O221.2

SHANG Yu-feng,, YU Bo. Boundary Moving Combined Homotopy Method for Nonconvex Nonlinear Programming and Its Convergence[J].J4, 2006, 44(03): 357-361.

[1]	WANG Cailing, YANG Xue. Duality of Invex Convex Multiobjective Programming [J]. Journal of Jilin University Science Edition, 2016, 54(02): 276-278.
[2]	LIU Yubao, QIN Guihe. Adaptive Differential Evolution Algorithm forReliability Redundancy Optimization [J]. Journal of Jilin University Science Edition, 2016, 54(01): 70-76.
[3]	QU Hongyan, GUAN Lihong, WANG Mingming, WANG Xiuyu. Existence Condition of a Solution of GeneralVariational Inequality Problem [J]. Journal of Jilin University Science Edition, 2015, 53(06): 1197-1200.
[4]	LI Jianhua, LI Zipeng, LV Xianrui, ZHANG Hui. A PrimalDual Interior Point Method with Parameter Perturbationfor Solving a Class of General Nonlinear Programming Problems [J]. Journal of Jilin University Science Edition, 2015, 53(06): 1099-1104.
[5]	LIU Wei, XUE Dongmei. Complexity Analysis for the Homotopy Method of Non-convexProgramming under Normal Cone Conditions [J]. Journal of Jilin University Science Edition, 2014, 52(06): 1203-1206.
[6]	HE Li, TAN Jiawei, CHEN Jia, LIU Qinghuai. Aggregate Homotopy InteriorPoint Method forMultiobjective Programming Problem withEquality and Inequality Constraints [J]. Journal of Jilin University Science Edition, 2014, 52(02): 212-218.
[7]	JIN Jian-Lu, TAN Jia-Wei, HE Chi, LIU Qiang-Fu. Aggregate Homotopy InteriorPoint Method forGeneral Nonlinear Programming Problems [J]. J4, 2011, 49(06): 1044-1052.
[8]	JIANG Zhi-Xia, LI Jun, ZHANG Shan. An Improved Primaldual Point Method [J]. J4, 2009, 47(4): 677-682.
[9]	FENG Zixuan, WANG Cailing, JI Shuguan. Interiorpoint QuasiNewton Method of Modified Augmented Lagrangian Function [J]. J4, 2009, 47(02): 245-247.
[10]	SUN Wenjuan, LIU Qinghuai, WANG Cailing. Homotopy Method for Getting a Local Minimum ofa Class of Nonconvex Programming [J]. J4, 2008, 46(03): 469-471.
[11]	ZHANG Shan, JIANG Zhixia,, LIU Yuanhui. Primaldual Point Method for Nonlinear Programming [J]. J4, 2007, 45(05): 717-722.
[12]	YANG Yihua, ZHAO Liqin, LV Xianrui, LIU Shuyuan, SONG Zhao. A Combined Homotopy Method under Quasicone Conditionfor Nonconvex Nonlinear Programming with Equality and Inequality Constrains [J]. J4, 2007, 45(04): 535-538.
[13]	YANG Yihua, LV Xianrui, LIU Qinghuai. Infeasible Interiorpoint-Homotopy Method for Non-convex Programming under Normal Cone Condition [J]. J4, 2007, 45(03): 365-368.
[14]	YANG Yihua, ZHAO Li qin, LV Xianrui, LIU Qinghuai. The Aggregate Homotopy Interiorpoint Methodfor Multi-objective Convex Programming [J]. J4, 2006, 44(06): 883-887.
[15]	YANG Yi-hua, LV Xian-rui, LIU Qing-huai, ZHENG Zhi-ying. Homotopy-interior Point Algorithm for Solving Set of Effective Solutions of Double-objective Convex Programming [J]. J4, 2006, 44(01): 39-43.

Boundary Moving Combined Homotopy Method for Nonconvex Nonlinear Programming and Its Convergence

PDF (PC)

Like

Knowledge

Abstract

Cite this article

share this article

References

Related Articles 15

Metrics

Comments

Recommended 10