The simple integer recourse (SIR) function of a decision variable is the expectation of the integer roundup of the shortage/surplus between a random variable with a known distribution and the decision variable. It is the integer analogue of the simple (continuous) recourse function in two stage stochastic linear programming. Structural properties and approximations of SIR functions have been ex...

We propose an algorithm for multistage stochastic linear programs with recourse where random quantities in different stages are independent. The algorithm approximates successively expected recourse functions by building up valid cutting planes to support these functions from below. In each iteration, for the expected recourse function in each stage, one cutting plane is generated using the dua...

We consider nonlinear multistage stochastic optimization problems in the spaces of integrable functions. allow for dynamics and general objective functionals, including dynamic risk measures. study causal operators describing system derive Clarke subdifferential a penalty function involving such operators. Then we introduce concept subregular recourse establish subregularity resulting systems t...

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...