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

Abstract

We study a new class of optimization problems calledstochastic separated continuous conic programming(SSCCP). SSCCP is an extension to the optimization model calledseparated 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.