Stochastic Methods Based on VU-Decomposition Methods for Stochastic Convex Minimax Problems

Lu Yuan; Wang Wei; Chen Shuang; Huang Ming

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Stochastic Methods Based on VU-Decomposition Methods for Stochastic Convex Minimax Problems

机译：基于VU分解法的随机凸最小极大问题的随机方法

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This paper applies sample average approximation (SAA) method based on VU-space decomposition theory to solve stochastic convex minimax problems. Under some moderate conditions, the SAA solution converges to its true counterpart with probability approaching one and convergence is exponentially fast with the increase of sample size. Based on the VU-theory, a superlinear convergent VU-algorithm frame is designed to solve the SAA problem.

机译：本文采用基于VU空间分解理论的样本平均逼近（SAA）方法来解决随机凸极小极大问题。在某些适度的条件下，SAA解决方案收敛到其真实对应物，概率接近1，并且随着样本数量的增加，收敛速度呈指数级增长。基于VU理论，设计了一种超线性收敛的VU算法框架来解决SAA问题。

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《Mathematical Problems in Engineering》 |2014年第21期|894248.1-894248.5|共5页
作者
Lu Yuan; Wang Wei; Chen Shuang; Huang Ming;
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作者单位

Shenyang Univ, Normal Coll, Shenyang 110044, Peoples R China.;

Liaoning Normal Univ, Sch Math, Dalian 116029, Peoples R China.;

Dalian Univ Technol, Sch Math Sci, Dalian 116024, Peoples R China.;

Dalian Univ Technol, Sch Math Sci, Dalian 116024, Peoples R China.;

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1. Stochastic Methods Based onVU-Decomposition Methods for Stochastic Convex Minimax Problems [J] . YuanLu, WeiWang, ShuangChen, Mathematical Problems in Engineering: Theory, Methods and Applications . 2014,第3期

机译：基于VU分解法的随机凸极小极大问题的随机方法
2. CONVERGENCE ANALYSIS OF SAMPLING-BASED DECOMPOSITION METHODS FOR RISK-AVERSE MULTISTAGE STOCHASTIC CONVEX PROGRAMS [J] . Guigues Vincent SIAM Journal on Optimization: A Publication of the Society for Industrial and Applied Mathematics . 2016,第4期

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6. Stochastic θ-Methods for a Class of Jump-Diffusion Stochastic Pantograph Equations with Random Magnitude [O] . Hua Yang, Feng Jiang -1

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7. Convergence analysis of sampling-based decomposition methods for risk-averse multistage stochastic convex programs [O] . Guigues, Vincent 2016

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Stochastic Methods Based on VU-Decomposition Methods for Stochastic Convex Minimax Problems

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