Expected-value-constrained programming (ECP) formulations are a broad class of stochastic programming problems including integrated chance constraints, risk models, and stochastic dominance formulations. Given the wide availability of data, it is common in applications to have independent contextual information associated with the target or dependent random variables of the problem. We show how to incorporate such … Read more
Commonly, decomposition and splitting techniques for optimization problems strongly depend on convexity. Implementable splitting methods for nonconvex and nonsmooth optimization problems are scarce and often lack convergence guarantees. Among the few exceptions is the Progressive Decoupling Algorithm (PDA), which has local convergence should convexity be elicitable. In this work, we furnish PDA with a descent … Read more
We consider Benders decomposition algorithms for multistage stochastic mixed-integer programs (SMIPs) with general mixed-integer decision variables at every node in the scenario tree. We derive a hierarchy of convex polyhedral lower bounds for the value functions and expected cost to-go functions in multistage SMIPs using affine parametric cutting planes in extended spaces for the feasible … Read more
We consider the chance-constrained program (CCP) with random right-hand side under a finite discrete distribution. It is known that the standard mixed integer linear programming (MILP) reformulation of the CCP is generally difficult to solve by general-purpose solvers as the branch-and-cut search trees are enormously large, partly due to the weak linear programming relaxation. In … Read more
Gradient computation of multivariate distribution functions calls for considerable effort. A standard procedure is component-wise computation, hence coordinate descent is an attractive choice. This paper deals with constrained convex problems. We apply random coordinate descent in an approximation scheme that is an inexact cutting-plane method from a dual viewpoint. We present convergence proofs and a … Read more
A traditional stochastic program under a finite population typically seeks to optimize efficiency by maximizing the expected profits or minimizing the expected costs, subject to a set of constraints. However, implementing such optimization-based decisions can have varying impacts on individuals, and when assessed using the individuals’ utility functions, these impacts may differ substantially across demographic … Read more
In this paper, we examine two-stage stochastic quadratic programming problems, where the objective function of the first and second stages are quadratic functions, and the constraints are linear. The uncertainty is associated with the second-stage right-hand side and variable bounds. In large-scale settings, when the number of scenarios necessary to represent the underlying stochastic process … Read more
One of the chief attractions of stochastic mixed-integer second-order cone programming is its diverse applications, especially in engineering (Alzalg and Alioui, {\em IEEE Access}, 10:3522-3547, 2022). The linear and nonlinear versions of this class of optimization problems are still unsolved yet. In this paper, we develop a hybrid optimization algorithm coupling branch-and-bound and primal-dual interior-point … Read more
In the context of optimization under uncertainty, we consider various combinations of distribution estimation and resampling (bootstrap and bagging) for obtaining samples used to acquire a solution and for computing a confidence interval for an optimality gap. This paper makes three experimental contributions to on-going research in data driven stochastic programming: a) most of the … Read more
Stochastic programming (SP) is a well-studied framework for modeling optimization problems under uncertainty. However, despite the significant advancements in solving large SP models, they are not widely used in industrial practice, often because SP solutions are difficult to understand and hence not trusted by the user. Unlike deterministic optimization models, SP models generally involve recourse … Read more