Stochastic optimization, especially multistage models, is well known to be computationally excruciating. In this paper, we introduce the concept of semi-complete recourse in the context of stochastic programming as a less restrictive condition compared to complete recourse and propose methods for approximating multistage stochastic programs with risk constraints and semi-complete recourse. We e...

Existing complexity results in stochastic linear programming using the Turing model depend only on problem dimensionality. We apply techniques from the information-based complexity literature to show that the smoothness of the recourse function is just as important. We derive approximation error bounds for the recourse function of two-stage stochastic linear programs and show that their worst c...

We introduce two-stage stochastic semidefinite programs with recourse and present a Benders decomposition based linearly convergent interior point algorithms to solve them. This extends the results in Zhao [16] wherein it was shown that the logarithmic barrier associated with the recourse function of two-stage stochastic linear programs with recourse behaves as a strongly self-concordant barrie...

Zhao [28] recently showed that the log barrier associated with the recourse function of twostage stochastic linear programs behaves as a strongly self-concordant barrier and forms a self concordant family on the first stage solutions. In this paper we show that the recourse function is also strongly self-concordant and forms a self concordant family for the two-stage stochastic convex quadratic...

We review convex approximations for stochastic programs with simple integer recourse. Both for the case of discrete and continuous random variables such approximations are discussed, and representations as continuous simple recourse problems are given.

Ariyawansa and Zhu have introduced a class of volumetric barrier decomposition algorithms [5] for solving two-stage stochastic semidefinite programs with recourse (SSDPs) [4]. In this paper we utilize their work for SSDPs to derive a class of volumetric barrier decomposition algorithms for solving two-stage stochastic quadratic programs with recourse and to establish polynomial complexity of ce...

This paper introduces disjunctive decomposition for two-stage mixed 0-1 stochastic integer programs (SIPs) with random recourse. Disjunctive decomposition allows for cutting planes based on disjunctive programming to be generated for each scenario subproblem under a temporal decomposition setting of the SIP problem. A new class of valid inequalities for mixed 0-1 SIP with random recourse is pre...

This paper deals with day-ahead programming under uncertainties in microgrids (MGs). A two-stage stochastic programming with the fixed recourse approach was adopted. The studied MG was considered in the grid-connected mode with the capability of power exchange with the upstream network. Uncertain electricity market prices, unpredictable load demand, and uncertain wind and solar power values, du...