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.

Endogenous, i.e. decision-dependent, uncertainty has received increased interest in the stochastic programming community. In robust optimization context, however, it rarely been considered. This work addresses multistage mixed-integer with decision-dependent sets. The proposed framework allows us to consider both continuous and integer recourse, including recourse decisions that affect set. We ...

Mathematical programming has been applied to various problems. For many actual problems, the assumption that the parameters involved are deterministic known data is often unjustified. In such cases, these data contain uncertainty and are thus represented as random variables, since they represent information about the future. Decision-making under uncertainty involves potential risk. Stochastic ...

We present a unified and tractable framework for distributionally robust optimization that could encompass a variety of statistical information including, among others things, constraints on expectation, conditional expectation, and disjoint confidence sets with uncertain probabilities defined by φ-divergence. In particular, we also show that the Wasserstein-based ambiguity set has an equivalen...

In the last decade, multi-stage stochastic programs with recourse have been broadly used to model real-world applications. This paper reviews the main optimization methods that are used to solve multi-stage stochastic programs with recourse. In particular, this paper reviews four types of optimization approaches to solve multi-stage stochastic programs with recourse: direct methods, decompositi...

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...

We consider the objective function of a simple recourse problem with fixed technology matrix and integer second-stage variables. Separability due to the simple recourse structure allows to study a one-dimensional version instead. Based on an explicit formula for the objective function, we derive a complete description of the class of probability density functions such that the objective functio...