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In this paper, we propose a multilevel stochastic framework for the solution of nonconvex unconstrained optimization problems. The proposed approach uses random regularized first-order models that exploit an available hierarchical…
This paper studies the problem of globally optimizing a variable of interest that is part of a causal model in which a sequence of interventions can be performed. This problem arises in biology, operational research, communications and,…
We propose new sequential simulation-optimization algorithms for general convex optimization via simulation problems with high-dimensional discrete decision space. The performance of each choice of discrete decision variables is evaluated…
The recently developed Distributed Block Proximal Method, for solving stochastic big-data convex optimization problems, is studied in this paper under the assumption of constant stepsizes and strongly convex (possibly non-smooth) local…
This paper considers the problem of minimizing a convex expectation function with a set of inequality convex expectation constraints. We present a computable stochastic approximation type algorithm, namely the stochastic linearized proximal…
This paper focuses on finding approximate solutions to stochastic optimal control problems with control domains being not necessarily convex, where the state trajectory is subject to controlled stochastic differential equations. The…
This paper considers a general problem of convex stochastic optimization in a relatively low-dimensional space (e.g., 100 variables). It is known that for deterministic convex optimization problems of small dimensions, the fastest…
In this paper, we propose a stochastic method for solving equality constrained optimization problems that utilizes predictive variance reduction. Specifically, we develop a method based on the sequential quadratic programming paradigm that…
We develop and analyze stochastic optimization algorithms for problems in which the expected loss is strongly convex, and the optimum is (approximately) sparse. Previous approaches are able to exploit only one of these two structures,…
Sequential quadratic optimization algorithms are proposed for solving smooth nonlinear optimization problems with equality constraints. The main focus is an algorithm proposed for the case when the constraint functions are deterministic,…
A widely used heuristic for solving stochastic optimization problems is to use a deterministic rolling horizon procedure, which has been modified to handle uncertainty (e.g. buffer stocks, schedule slack). This approach has been criticized…
In this paper, we propose new sequential randomized algorithms for convex optimization problems in the presence of uncertainty. A rigorous analysis of the theoretical properties of the solutions obtained by these algorithms, for full…
Price determination is a central research topic of revenue management in marketing. The important aspect in pricing is controlling the stochastic behavior of demand, and the previous studies have tackled price optimization problems with…
Bayesian optimization is a class of data efficient model based algorithms typically focused on global optimization. We consider the more general case where a user is faced with multiple problems that each need to be optimized conditional on…
Black-box optimization problems often require simultaneously optimizing different types of variables, such as continuous, integer, and categorical variables. Unlike integer variables, categorical variables do not necessarily have a…
Distributed stochastic optimization has drawn great attention recently due to its effectiveness in solving large-scale machine learning problems. Though numerous algorithms have been proposed and successfully applied to general practical…
In this paper we analyze several new methods for solving nonconvex optimization problems with the objective function formed as a sum of two terms: one is nonconvex and smooth, and another is convex but simple and its structure is known.…
We introduce the online stochastic Convex Programming (CP) problem, a very general version of stochastic online problems which allows arbitrary concave objectives and convex feasibility constraints. Many well-studied problems like online…
Chance constrained program is computationally intractable due to the existence of chance constraints, which are randomly disturbed and should be satisfied with a probability. This paper proposes a two-layer randomized algorithm to address…
We consider convex stochastic optimization problems under different assumptions on the properties of available stochastic subgradient. It is known that, if the value of the objective function is available, one can obtain, in parallel,…