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Mathematical Problems in Engineering
Volume 2014 (2014), Article ID 896591, 20 pages
http://dx.doi.org/10.1155/2014/896591
Research Article

Stochastic Separated Continuous Conic Programming: Strong Duality and a Solution Method

Lingnan (University) College, Sun Yat-sen University, Guangzhou, Guangdong 510275, China

Received 3 November 2013; Accepted 29 November 2013; Published 9 January 2014

Academic Editor: Dongdong Ge

Copyright © 2014 Xiaoqing Wang. 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 study a new class of optimization problems called stochastic separated continuous conic programming (SSCCP). SSCCP is an extension to the optimization model called separated continuous conic programming (SCCP) which has applications in robust optimization and sign-constrained linear-quadratic control. Based on the relationship among SSCCP, its dual, and their discretization counterparts, we develop a strong duality theory for the SSCCP. We also suggest a polynomial-time approximation algorithm that solves the SSCCP to any predefined accuracy.