While deterministic optimization enjoys an almost universally accepted canonical form, stochastic optimization is a jungle of competing notational systems and algorithmic strategies. This is especially problematic in the context of sequential (multistage) stochastic optimization problems, which is the focus of our presentation. In this article, we place a variety of competing strategies into a ...

In this paper we consider interchangeability of the minimization operator with monotone risk functionals. In particular we discuss the role of strict monotonicity of the risk functionals. We also discuss implications to solutions of dynamic programming equations of risk averse multistage stochastic programming problems.

In this paper we consider the adjustable robust approach to multistage optimization, for which we derive dynamic programming equations. We also discuss this from a point of view of risk averse stochastic programming. As an example we consider a robust formulation of the classical inventory model and show that, similar to the risk neutral case, a basestock policy is optimal.

Many decisions involve multiple stages of choices and events. In this paper to develops fuzzy dynamic system approach for solving multistage decision-making problems. Fuzzy dynamic system is a promising tool for dealing with multistage decision-making and optimization problems under fuzziness. The cases of deterministic, stochastic, fuzzy dynamic system, fuzzy criterion set dynamic programming,...

We consider risk-averse formulations of multistage stochastic linear programs. For these formulations, based on convex combinations of spectral risk measures, risk-averse dynamic programming equations can be written. As a result, the Stochastic Dual Dynamic Programming (SDDP) algorithm can be used to obtain approximations of the corresponding risk-averse recourse functions. This allows us to de...

Uncertainties are widespread in the optimization of process systems, such as uncertainties technologies, prices, and customer demands. In this paper, we review basic concepts recent advances a risk-neutral mathematical framework called “stochastic programming” its applications solving systems engineering problems under uncertainty. This intends to provide both tutorial for beginners without pri...

We consider well-known decomposition techniques for multistage stochastic programming and a new scheme based on normal solutions for stabilizing calculations as the iteration process progresses. The given algorithms combine ideas from finite perturbation of convex programs and level bundle methods to regularize the so-called forward step of these decomposition methods. In contrast to other regu...

This paper presents a multistage stochastic linear programming problem solved by a stochastic nested Benders decomposition algorithm. The algorithm allows the node aggregation and division of the scenario tree into connected subtrees forming arbitrary subproblems that will be solved as the algorithm proceeds. Different aggregation strategies have been tested and numerical results of the applica...

This paper considers large-scale multistage stochastic linear programs. Sampling is incorporated into the nested decomposition algorithm in a manner which proves to be significantly more efficient than a previous approach. The main advantage of the method arises from maintaining a restricted set of solutions that substantially reduces computation time in each stage of the procedure. Dedicated t...