Chance constrained programming is an effective and convenient approach to control risk in decision making under uncertainty. However, due to unknown probability distributions of random parameters, the solution obtained from a chance constrained optimization problem can be biased. In practice, instead of knowing the true distribution of a random parameter, only a series of historical … Read more
In this paper we study new stochastic approximation (SA) type algorithms, namely, the accelerated SA (AC-SA), for solving strongly convex stochastic composite optimization (SCO) problems. Specifically, by introducing a domain shrinking procedure, we significantly improve the large-deviation results associated with the convergence rate of a nearly optimal AC-SA algorithm presented by the authors. Moreover, we … Read more
The Search Algorithms have been introduced in the paper [3][6] under the name ‘Search via Probability Algorithm’. These optimization techniques converge very fast and are very efficient for solving optimization problems with very large scale feasible domains. But these optimization techniques are not effective in solving the numerical optimization problems with long narrow feasible domains. … Read more
We consider the solution of a system of stochastic generalized equations (SGE) where the underlying functions are mathematical expectation of random set-valued mappings. SGE has many applications such as characterizing optimality conditions of a nonsmooth stochastic optimization problem and a stochastic equilibrium problem. We derive quantitative continuity of expected value of the set-valued mapping with … Read more
In this paper, we introduce a new stochastic approximation (SA) type algorithm, namely the randomized stochastic gradient (RSG) method, for solving an important class of nonlinear (possibly nonconvex) stochastic programming (SP) problems. We establish the complexity of this method for computing an approximate stationary point of a nonlinear programming problem. We also show that this … Read more
It is well known that most risk measures (risk functionals) are time inconsistent in the following sense: It may happen that today some loss distribution appears to be less risky than another, but looking at the conditional distribution at a later time, the opposite relation holds. In this article we demonstrate that this time inconsistency … Read more
The approximation of stochastic processes by trees is an important topic in multistage stochastic programming. In this paper we focus on improving the approximation of large trees by smaller (tractable) trees. The quality of the approximation is measured by the nested distance, recently introduced in [Pflug]. The nested distance is derived from the Wasserstein distance. … Read more
We consider a chance-constrained optimization problem (CCOP), where the random variables follow finite discrete distributions. The problem is in general nonconvex and can be reformulated as a mixed-integer program. By exploiting the special structure of the probabilistic constraint, we propose an alternating direction method for finding suboptimal solutions of CCOP. At each iteration, this method … Read more
We prove the almost-sure convergence of a class of sampling-based nested decomposition algorithms for multistage stochastic convex programs in which the stage costs are general convex functions of the decisions, and uncertainty is modelled by a scenario tree. As special cases, our results imply the almost-sure convergence of SDDP, CUPPS and DOASA when applied to … Read more
For many decision making problems under uncertainty, it is crucial to develop risk-averse models and specify the decision makers’ risk preferences based on multiple stochastic performance measures (or criteria). Incorporating such multivariate preference rules into optimization models is a fairly recent research area. Existing studies focus on extending univariate stochastic dominance rules to the multivariate … Read more