Related papers: A Block-Activated Decomposition Algorithm for Mult…
Multistage stochastic optimization problems are, by essence, complex as their solutions are indexed both by stages and by uncertainties. Their large scale nature makes decomposition methods appealing, like dynamic programming which is a…
Under consideration are multicomponent minimization problems involving a separable nonsmooth convex function penalizing the components individually, and nonsmooth convex coupling terms penalizing linear mixtures of the components. We…
In this study, we consider two classes of multicriteria two-stage stochastic programs in finite probability spaces with multivariate risk constraints. The first-stage problem features a multivariate stochastic benchmarking constraint based…
A block decomposition method is proposed for minimizing a (possibly non-convex) continuously differentiable function subject to one linear equality constraint and simple bounds on the variables. The proposed method iteratively selects a…
Multi-objective optimization is central to many engineering and machine learning applications, where multiple objectives must be optimized in balance. While multi-gradient based optimization methods combine these objectives in each step,…
This paper proposes an algorithm to efficiently solve multistage stochastic programs with block separable recourse where each recourse problem is a multistage stochastic program with stage-wise independent uncertainty. The algorithm first…
We consider stochastic variational inequalities with monotone operators defined as the expected value of a random operator. We assume the feasible set is the intersection of a large family of convex sets. We propose a method that combines…
We propose stochastic splitting algorithms for solving large-scale composite inclusion problems involving monotone and linear operators. They activate at each iteration blocks of randomly selected resolvents of monotone operators and,…
Constrained non-convex optimization problems frequently arise in control applications. Solving such problems is inherently challenging, as existing methods often converge to suboptimal local minima or incur prohibitive computational costs.…
An algorithm is proposed, analyzed, and tested experimentally for solving stochastic optimization problems in which the decision variables are constrained to satisfy equations defined by deterministic, smooth, and nonlinear functions. It is…
We propose new primal-dual decomposition algorithms for solving systems of inclusions involving sums of linearly composed maximally monotone operators. The principal innovation in these algorithms is that they are block-iterative in the…
In this paper, a class of large-scale distributed nonsmooth convex optimization problem over time-varying multi-agent network is investigated. Specifically, the decision space which can be split into several blocks of convex set is…
We introduce a relaxed-projection splitting algorithm for solving variational inequalities in Hilbert spaces for the sum of nonsmooth maximal monotone operators, where the feasible set is defined by a nonlinear and nonsmooth continuous…
In this paper, we explore a specific optimization problem that combines a differentiable nonconvex function with a nondifferentiable function for multi-block variables, which is particularly relevant to tackle the multilinear…
We consider a class of sampling-based decomposition methods to solve risk-averse multistage stochastic convex programs. We prove a formula for the computation of the cuts necessary to build the outer linearizations of the recourse…
In approximating solutions of nonstationary problems, various approaches are used to compute the solution at a new time level from a number of simpler (sub-)problems. Among these approaches are splitting methods. Standard splitting schemes…
The stochastic gradient (SG) method can minimize an objective function composed of a large number of differentiable functions, or solve a stochastic optimization problem, to a moderate accuracy. The block coordinate descent/update (BCD)…
Multi-stage stochastic programming is a well-established framework for sequential decision making under uncertainty by seeking policies that are fully adapted to the uncertainty. Often such flexible policies are not desirable, and the…
Stochastic gradient methods are scalable for solving large-scale optimization problems that involve empirical expectations of loss functions. Existing results mainly apply to optimization problems where the objectives are one- or two-level…
Multistage stochastic programming is a powerful tool allowing decision-makers to revise their decisions at each stage based on the realized uncertainty. However, in practice, organizations are not able to be fully flexible, as decisions…