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We study randomized algorithms for constrained optimization, in abstract frameworks that include, in strictly increasing generality: convex programming; LP-type problems; violator spaces; and a setting we introduce, consistent spaces. Such…
We study a class of nonconvex-nonconcave minimax problems in which the inner maximization problem satisfies a local Kurdyka-Lojasiewicz (KL) condition that may vary with the outer minimization variable. In contrast to the global KL or…
Peak Estimation aims to find the maximum value of a state function achieved by a dynamical system. This problem is non-convex when considering standard Barrier and Density methods for invariant sets, and has been treated heuristically by…
In optimization-based approaches to inverse problems and to statistical estimation, it is common to augment criteria that enforce data fidelity with a regularizer that promotes desired structural properties in the solution. The choice of a…
Separable convex optimization problems with linear ascending inequality and equality constraints are addressed in this paper. Under an ordering condition on the slopes of the functions at the origin, an algorithm that determines the optimum…
We consider an expected-value ranking and selection (R&S) problem where all k solutions' simulation outputs depend on a common parameter whose uncertainty can be modeled by a distribution. We define the most probable best (MPB) to be the…
This paper develops and compares algorithms to compute inner approximations of the Minkowski sum of convex polytopes. As an application, the paper considers the computation of the feasibility set of aggregations of distributed energy…
We consider the problem of analyzing the probabilistic performance of first-order methods when solving convex optimization problems drawn from an unknown distribution only accessible through samples. By combining performance estimation…
We first describe a general class of optimization problems that describe many natural, economic, and statistical phenomena. After noting the existence of a conserved quantity in a transformed coordinate system, we outline several instances…
In this paper, we compute the tightest possible bounds on the probability that the optimal value of a combinatorial optimization problem in maximization form with a random objective exceeds a given number, assuming only knowledge of the…
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…
Several optimization schemes have been known for convex optimization problems. However, numerical algorithms for solving nonconvex optimization problems are still underdeveloped. A progress to go beyond convexity was made by considering the…
In this paper, we propose new proximal Newton-type methods for convex optimization problems in composite form. The applications include model predictive control (MPC) and embedded MPC. Our new methods are computationally attractive since…
The Performance Estimation Problem (PEP) approach consists in computing worst-case performance bounds on optimization algorithms by solving an optimization problem: one maximizes an error criterion over all initial conditions allowed and…
This paper analyzes the convergence rates of the {\it Frank-Wolfe } method for solving convex constrained multiobjective optimization. We establish improved convergence rates under different assumptions on the objective function, the…
Optimality conditions in the form of a variational inequality are proved for a class of constrained optimal control problems of stochastic differential equations. The cost function and the inequality constraints are functions of the…
We introduce the concepts of max-closedness and numeraires of convex subsets in the nonnegative orthant of the topological vector space of all random variables built over a probability space, equipped with a topology consistent with…
Particle gradient descent, which uses particles to represent a probability measure and performs gradient descent on particles in parallel, is widely used to optimize functions of probability measures. This paper considers particle gradient…
Submodular maximization generalizes many fundamental problems in discrete optimization, including Max-Cut in directed/undirected graphs, maximum coverage, maximum facility location and marketing over social networks. In this paper we…
This paper considers an extension of the multivariate symmetric Laplace distribution to matrix variate case. The symmetric Laplace distribution is a scale mixture of normal distribution. The maximum likelihood estimators (MLE) of the…