相关论文: Sample Average Approximations of Strongly Convex S…

We prove novel convergence results for a stochastic proximal gradient algorithm suitable for solving a large class of convex optimization problems, where a convex objective function is given by the sum of a smooth and a possibly non-smooth…

In this paper, a stochastic alternating direction method of multipliers (ADMM) is proposed for a class of nonsmooth composite and stochastic convex optimization problems in Hilbert space, motivated by optimization problems constrained by…

Large sectors of the recent optimization literature focused in the last decade on the development of optimal stochastic first order schemes for constrained convex models under progressively relaxed assumptions. Stochastic proximal point is…

We propose a stochastic approximation method for approximating the efficient frontier of chance-constrained nonlinear programs. Our approach is based on a bi-objective viewpoint of chance-constrained programs that seeks solutions on the…

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…

A classic result by Cook, Gerards, Schrijver, and Tardos provides an upper bound of $n \Delta$ on the proximity of optimal solutions of an Integer Linear Programming problem and its standard linear relaxation. In this bound, $n$ is the…

We study the problem of minimizing the average of a very large number of smooth functions, which is of key importance in training supervised learning models. One of the most celebrated methods in this context is the SAGA algorithm. Despite…

We study system design problems stated as parameterized stochastic programs with a chance-constraint set. We adopt a Bayesian approach that requires the computation of a posterior predictive integral which is usually intractable. In…

In this paper, we study a class of bilevel programming problem where the inner objective function is strongly convex. More specifically, under some mile assumptions on the partial derivatives of both inner and outer objective functions, we…

Sparse polynomial approximation has become indispensable for approximating smooth, high- or infinite-dimensional functions from limited samples. This is a key task in computational science and engineering, e.g., surrogate modelling in…

We consider stochastic optimization problems which use observed data to estimate essential characteristics of the random quantities involved. Sample average approximation (SAA) or empirical (plug-in) estimation are very popular ways to use…

We consider constrained optimization problems with a nonsmooth objective function in the form of mathematical expectation. The Sample Average Approximation (SAA) is used to estimate the objective function and variable sample size strategy…

We study the regret performance of Sample Average Approximation (SAA) for data-driven newsvendor problems with general convex inventory costs. In literature, the optimality of SAA has not been fully established under both \alpha-global…

We construct a new tail bound for the sum of independent random variables for situations in which the expected value of the sum is known and each random variable lies within a specified interval, which may be different for each variable.…

A computationally efficient method to solve non-convex programming problems with linear equality constraints is presented. The proposed method is based on a recursively feasible and descending sequential convex programming procedure proven…

Recent studies have shown that heavy tails can emerge in stochastic optimization and that the heaviness of the tails have links to the generalization error. While these studies have shed light on interesting aspects of the generalization…

We study the consistency of stochastic dynamic programs under converging probability distributions and other approximations. Utilizing results on the epi-convergence of expectation functions with varying measures and integrands, and the…

Stability and error analysis remain challenging for problems that lack regularity properties near solutions, are subject to large perturbations, and might be infinite dimensional. We consider nonconvex optimization and generalized equations…

This paper is concerned with a class of stochastic optimization problems defined on a Banach space with almost sure conic-type constraints. For this class of problems, we investigate the consistency of optimal values and solutions…

Stochastic approximation is one of the effective approach to deal with the large-scale machine learning problems and the recent research has focused on reduction of variance, caused by the noisy approximations of the gradients. In this…