Related papers: Robust approximation of chance constrained optimiz…

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 introduce a novel approach to reduce the computational effort of solving mixed-integer convex chance constrained programs through the scenario approach. Instead of reducing the number of required scenarios, we directly minimize the…

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…

Standard results in stochastic convex optimization bound the number of samples that an algorithm needs to generate a point with small function value in expectation. More nuanced high probability guarantees are rare, and typically either…

We study two-stage adjustable robust linear programming in which the right-hand sides are uncertain and belong to a convex, compact uncertainty set. This problem is NP-hard, and the affine policy is a popular, tractable approximation. We…

Many applications using large datasets require efficient methods for minimizing a proximable convex function subject to satisfying a set of linear constraints within a specified tolerance. For this task, we present a proximal projection…

Robust estimation is much more challenging in high dimensions than it is in one dimension: Most techniques either lead to intractable optimization problems or estimators that can tolerate only a tiny fraction of errors. Recent work in…

This paper discusses a novel probabilistic approach for the design of robust model predictive control (MPC) laws for discrete-time linear systems affected by parametric uncertainty and additive disturbances. The proposed technique is based…

This work proposes and analyzes a compressed sensing approach to polynomial approximation of complex-valued functions in high dimensions. Of particular interest is the setting where the target function is smooth, characterized by a rapidly…

We use a Monte Carlo method to assemble finite element matrices for polynomial Chaos approximations of elliptic equations with random coefficients. In this approach, all required expectations are approximated by a Monte Carlo method. The…

Robust topology optimization (RTO), as a class of topology optimization problems, identifies a design with the best average performance while reducing the response sensitivity to input uncertainties, e.g. load uncertainty. Solving RTO is…

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…

Chance-constrained programs (CCP) represent a trade-off between conservatism and robustness in optimization. In many CCPs, one optimizes an objective under a probabilistic constraint continuously parameterized by a random vector $\xi$. In…

With neural networks being used to control safety-critical systems, they increasingly have to be both accurate (in the sense of matching inputs to outputs) and robust. However, these two properties are often at odds with each other and a…

Two-stage stochastic optimization is a framework for modeling uncertainty, where we have a probability distribution over possible realizations of the data, called scenarios, and decisions are taken in two stages: we make first-stage…

Submodular optimization generalizes many classic problems in combinatorial optimization and has recently found a wide range of applications in machine learning (e.g., feature engineering and active learning). For many large-scale…

This paper presents an algorithmic study of a class of covering mixed-integer linear programming problems which encompasses classic cover problems, including multidimensional knapsack, facility location and supplier selection problems. We…

We consider the problem of analyzing and designing gradient-based discrete-time optimization algorithms for a class of unconstrained optimization problems having strongly convex objective functions with Lipschitz continuous gradient. By…

Chance constraints are frequently used to limit the probability of constraint violations in real-world optimization problems where the constraints involve stochastic components. We study chance-constrained submodular optimization problems,…

An integrated optimization method based on the constrained multi-objective evolutionary algorithm (MOEA) and non-intrusive polynomial chaos expansion (PCE) is proposed, which solves robust multi-objective optimization problems under…