求解最小体积轴向椭球问题的线性收敛算法

J4 ›› 2011, Vol. 49 ›› Issue (02): 173-178.

Previous Articles Next Articles

Linearly Convergent Algorithm for Solvingthe Minimum Volume AxisAligned Ellipsoid Problem

CONG Weijie, LIU Hongwei

School of Science, Xidian University, Xi’an 710071, China

Received:2010-06-02 Online:2011-03-26 Published:2011-06-14
Contact: LIU Hongwei E-mail:hwliu@mail.xidian.edu.cn

Abstract

Abstract:

Firstly, two approximate optimality conditions of the minimum volume axisaligned ellipsoid (MVAE) problem were defined. Secondly, a new approximate solution satisfying the second approximate optimality condition was computed. Furthermore, an approximation algorithm for the MVAE problem was presented, which has the linear convergence. The numerical results show the efficiency of the algorithm.

Key words: minimum volume axisaligned ellipsoid, optimality conditions, approximation algorithm, linear convergence

CLC Number:

O221.2

CONG Wei-Jie, LIU Gong-Wei. Linearly Convergent Algorithm for Solvingthe Minimum Volume AxisAligned Ellipsoid Problem[J].J4, 2011, 49(02): 173-178.

[1]	LIU Rui, LIU Qilong, CHEN Zhen. Iterative Algorithm with Linear Convergence Rate [J]. Journal of Jilin University Science Edition, 2019, 57(5): 1081-1087.
[2]	YAN Chunlei. Nonsmooth Multiobjective Programming underGeneralized V-r-Type-Ⅰ Invexity [J]. Journal of Jilin University Science Edition, 2014, 52(04): 687-692.
[3]	LUO Bin, WANG Lianming, ZHANG Mou. Image Space Analysis for Vector OptimizationProblem with Constraints [J]. Journal of Jilin University Science Edition, 2013, 51(06): 1068-1072.
[4]	CONG Wei-Jie. SMOType Algorithm for Solving the WeightedEuclidean OneCenter Problem [J]. J4, 2013, 51(03): 403-407.
[5]	WANG Cai-Ling, GAO Hui-Yan. Optimality Conditions of Vector Optimization ProblermsBased on the Weakly Convex [J]. J4, 2013, 51(02): 247-249.
[6]	WANG Cailing, GAO Huiyan. Optimality Conditions of Multiobjective Programming Problerms Based on the Astract Convexity [J]. J4, 2012, 50(4): 698-700.
[7]	WANG Cailing, LU Xiu shuang. Optimality Condition of a Class of Generalized Invex Functions [J]. J4, 2012, 50(01): 6-10.
[8]	WANG Cai-Ling. SaddlePoint Theory of Nonsmooth Invex Multiobjective Programming [J]. J4, 2011, 49(04): 693-695.
[9]	WANG Cailing, SUN Wenjuan, YANG Rong, WANG Xiaoling. Optimality Conditions of Nonsmooth Composite Generalized Invex Multiobjective Programming [J]. J4, 2008, 46(05): 877-879.

Linearly Convergent Algorithm for Solvingthe Minimum Volume AxisAligned Ellipsoid Problem

PDF (PC)

Like

Knowledge

Abstract

Cite this article

share this article

References

Related Articles 9

Metrics

Comments

Recommended 10