Our goal in this talk is to present unifying concepts for both stochastic and robust optimization problems involving infinite uncertainty sets. We apply methods from vector optimization in general spaces, set-valued optimization and scalarization techniques to develop a unified characterization of different concepts of robust optimization and stochastic programming. These methods provide new in...

We present a logical framework to represent and reason about stochastic optimization problems based on probability answer set programming [Saad and Pontelli, 2006; Saad, 2006; Saad, 2007a]. This is established by allowing probability optimization aggregates, e.g., minimum and maximum in the language of probability answer set programming to allow minimization or maximization of some desired crit...

In this paper we consider the notion of rectangularity of a set of probability measures, introduced in Epstein and Schneider [4], from a somewhat different point of view. We define rectangularity as a property of dynamic decomposition of a distributionally robust stochastic optimization problem and show how it relates to the modern theory of coherent risk measures. Consequently we discuss robus...

Recently, there has been a significant interest in introducing stochastic dominance relations as constraints into stochastic optimization problems. Optimization with first order stochastic dominance constraints in discrete distribution case can be formulated as mixed integer programs. In this article, we present a method to safely approximate such kinds of mixed integer programs. © 2009 World A...

Two general-purpose metaheuristic algorithms for solving multiobjective stochastic combinatorial optimization problems are introduced: SP-ACO (based on the Ant Colony Optimization paradigm) which combines the previously developed algorithms S-ACO and P-ACO, and SPSA, which extends Pareto Simulated Annealing to the stochastic case. Both approaches are tested on random instances of a TSP with tim...

We study PCA as a stochastic optimization problem and propose a novel stochastic approximation algorithm which we refer to as “Matrix Stochastic Gradient” (MSG), as well as a practical variant, Capped MSG. We study the method both theoretically and empirically.

Sequential quadratic optimization algorithms are proposed for solving smooth nonlinear problems with equality constraints. The main focus is an algorithm the case when the...

The escalating construction industry has led to a drastic increase in the dimension stone demand in the construction, mining and industry sectors. Assessment and investigation of mining projects and stone processing plants such as sawing machines is necessary to manage and respond to the sawing performance; hence, the soft computing techniques were considered as a challenging task due to stocha...

Stochastic programming is an optimization approach taking into account uncertainties in the system model. There are numerous possible applications of stochastic programming. The purpose of this short report is to introduce stochastic programming in simple, tutorial-like, terms. A simple example of an optimization of a covering gas demand is provided together with pointing out some fundamental p...

We give a simple proof of Strassen’s theorem on stochastic dominance using linear programming duality, without requiring measure-theoretic arguments. The result extends to generalized inequalities using conic optimization duality and provides an additional, intuitive optimization formulation for stochastic dominance.