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Journal of Function Spaces
Volume 2018 (2018), Article ID 3742575, 12 pages
https://doi.org/10.1155/2018/3742575
Research Article

Inexact SA Method for Constrained Stochastic Convex SDP and Application in Chinese Stock Market

1Information and Engineering College, Dalian University, Dalian, China
2School of Mathematical Sciences, Dalian University of Technology, Dalian, China
3School of Finance, Zhejiang University of Finance and Economics, Hangzhou, China

Correspondence should be addressed to Shuang Chen

Received 4 August 2017; Revised 17 November 2017; Accepted 13 December 2017; Published 23 January 2018

Academic Editor: Dhananjay Gopal

Copyright © 2018 Shuang Chen et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We propose stochastic convex semidefinite programs (SCSDPs) to handle uncertain data in applications. For these models, we design an efficient inexact stochastic approximation (SA) method and prove the convergence, complexity, and robust treatment of the algorithm. We apply the inexact method for solving SCSDPs where the subproblem in each iteration is only solved approximately and show that it enjoys the similar iteration complexity as the exact counterpart if the subproblems are progressively solved to sufficient accuracy. Numerical experiments show that the method we proposed was effective for uncertain problem.