The two-stage stochastic second-order cone programming (SSOCP) has been recently introduced in [Appl. Math. Model. 63, 5122–5134 (2012)] to cover a lot of important applications that cannot be captured by the two-stage stochastic linear programming (SLP). Wets [SIAM J. Applied Math. 14, 89–105 (1966)] described and characterized the equivalent convex program of the two-stage SLP. There is no work discussing the equivalent convex program of the two-stage SSOCP. The purpose of this short paper is to describe and characterize the equivalent convex program of the SSOCP problem.We first discuss the properties of the solution set of the SSOCP, and then develop the convex program equivalent to the SSOCP.We show that the objective function of the equivalent convex program is convex and continuous.
Digital Object Identifier (DOI)
Alabed Alhadi, Mohammad and Alzalg, Baha
"Stochastic Second-Order Cone Programming: The Equivalent Convex Program,"
Applied Mathematics & Information Sciences: Vol. 12:
3, Article 15.
Available at: https://digitalcommons.aaru.edu.jo/amis/vol12/iss3/15