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We developed a corporative stochastic approximation (CSA) type algorithm for semi-infinite programming (SIP), where the cut generation problem is solved inexactly. First, we provide general error bounds for inexact CSA. Then, we propose two…
An optimization algorithm for nonsmooth nonconvex constrained optimization problems with upper-C2 objective functions is proposed and analyzed. Upper-C2 is a weakly concave property that exists in difference of convex (DC) functions and…
This paper considers decentralized optimization of convex functions with mixed affine equality constraints involving both local and global variables. Constraints on global variables may vary across different nodes in the network, while…
When dealing with real-world optimization problems, decision-makers usually face high levels of uncertainty associated with partial information, unknown parameters, or complex relationships between these and the problem decision variables.…
In this paper, we present event constraints as a new modeling paradigm that generalizes joint chance constraints from stochastic optimization to (1) enforce a constraint on the probability of satisfying a set of constraints aggregated via…
Functional constraints and bi-functional constraints are an important constraint class in Constraint Programming (CP) systems, in particular for Constraint Logic Programming (CLP) systems. CP systems with finite domain constraints usually…
This paper considers the problem of minimizing an expectation function over a closed convex set, coupled with a {\color{black} functional or expectation} constraint on either decision variables or problem parameters. We first present a new…
This paper proposes a robust approximation method for solving chance constrained optimization (CCO) of polynomials. Assume the CCO is defined with an individual chance constraint that is affine in the decision variables. We construct a…
We study constrained stochastic programs where the decision vector at each time slot cannot be chosen freely but is tied to the realization of an underlying random state vector. The goal is to minimize a general objective function subject…
This paper is a study on solutions of the Sample Average Approximation Method to solve compound stochastic programs. We derive nonasymptotic upper estimates for probabilities of the approximation errors. The results depend on the sample…
This paper proposes a constrained stochastic successive convex approximation (CSSCA) algorithm to find a stationary point for a general non-convex stochastic optimization problem, whose objective and constraint functions are non-convex and…
Optimization models with non-convex constraints arise in many tasks in machine learning, e.g., learning with fairness constraints or Neyman-Pearson classification with non-convex loss. Although many efficient methods have been developed…
Two optimization algorithms are proposed for solving a stochastic programming problem for which the objective function is given in the form of the expectation of convex functions and the constraint set is defined by the intersection of…
We propose a novel distribution-free scheme to solve optimization problems where the goal is to minimize the expected value of a cost function subject to probabilistic constraints. Unlike standard sampling-based methods, our idea consists…
This paper investigates the stochastic program with the chance constraint on a quadratic form of random variables following multivariate Gaussian mixture distribution (GMD). Under some mild conditions, it is proved that the asymptotic…
We revisit the sample average approximation (SAA) approach for non-convex stochastic programming. We show that applying the SAA approach to problems with expected value equality constraints does not necessarily result in asymptotic…
We present a quasi-Newton method for unconstrained stochastic optimization. Most existing literature on this topic assumes a setting of stochastic optimization in which a finite sum of component functions is a reasonable approximation of an…
In this paper, we propose a unified convergence analysis for a class of generic shuffling-type gradient methods for solving finite-sum optimization problems. Our analysis works with any sampling without replacement strategy and covers many…
This paper proposes an algorithm to calculate the maximal probability of unsafety with respect to trajectories of a stochastic process and a hazard set. The unsafe probability estimation problem is cast as a primal-dual pair of…
We present a stochastic setting for optimization problems with nonsmooth convex separable objective functions over linear equality constraints. To solve such problems, we propose a stochastic Alternating Direction Method of Multipliers…