Related papers: Rockafellian Relaxation and Stochastic Optimizatio…

We consider the problem of computing a positive definite $p \times p$ inverse covariance matrix aka precision matrix $\theta=(\theta_{ij})$ which optimizes a regularized Gaussian maximum likelihood problem, with the elastic-net regularizer…

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…

This paper deals with shape optimization for elastic materials under stochastic loads. It transfers the paradigm of stochastic dominance, which allows for flexible risk aversion via comparison with benchmark random variables, from…

Optimization under uncertainty deals with the problem of optimizing stochastic cost functions given some partial information on their inputs. These problems are extremely difficult to solve and yet pervade all areas of technological and…

We consider various stochastic models that incorporate the notion of risk-averseness into the standard 2-stage recourse model, and develop novel techniques for solving the algorithmic problems arising in these models. A key notable feature…

Contextual stochastic optimization is an advanced methodology to model uncertainty in the presence of contextual information during decision planning processes. Although classical methodologies focus on minimizing the expectation of a…

In this paper, "chance optimization" problems are introduced, where one aims at maximizing the probability of a set defined by polynomial inequalities. These problems are, in general, nonconvex and computationally hard. With the objective…

We introduce a new approach to develop stochastic optimization algorithms for a class of stochastic composite and possibly nonconvex optimization problems. The main idea is to combine two stochastic estimators to create a new hybrid one. We…

We use a decision-theoretic framework to study the problem of forecasting discrete outcomes when the forecaster is unable to discriminate among a set of plausible forecast distributions because of partial identification or concerns about…

Approximations of optimization problems arise in computational procedures and sensitivity analysis. The resulting effect on solutions can be significant, with even small approximations of components of a problem translating into large…

A probabilistic framework is proposed for the optimization of efficient switched control strategies for physical systems dominated by stochastic excitation. In this framework, the equation for the state trajectory is replaced with an…

We develop a framework for convexifying a fairly general class of optimization problems. Under additional assumptions, we analyze the suboptimality of the solution to the convexified problem relative to the original nonconvex problem and…

Robust optimization safeguards decisions against uncertainty by optimizing against worst-case scenarios, yet their effectiveness hinges on a prespecified robustness level that is often chosen ad hoc, leading to either insufficient…

Providing generalization guarantees for stochastic optimization algorithms remains a key challenge in learning theory. Recently, numerous works demonstrated the impact of the geometric properties of optimization trajectories on…

This paper studies duality and optimality conditions in general convex stochastic optimization problems introduced by Rockafellar and Wets in 1976. We derive an explicit dual problem in terms of two dual variables, one of which is the…

We provide a novel computer-assisted technique for systematically analyzing first-order methods for optimization. In contrast with previous works, the approach is particularly suited for handling sublinear convergence rates and stochastic…

Robust Optimization has traditionally taken a pessimistic, or worst-case viewpoint of uncertainty which is motivated by a desire to find sets of optimal policies that maintain feasibility under a variety of operating conditions. In this…

In this article we present a general framework for non-concave robust stochastic control problems under model uncertainty in a discrete time finite horizon setting. Our framework allows to consider a variety of different path-dependent…

This study investigates a robust screening problem under distributional ambiguity, where a seller is uncertain about a buyer's true valuation distribution, knowing only that it lies near a reference distribution measured by the Wasserstein…

Regularization is a central tool for addressing ill-posedness in inverse problems and statistical estimation, with the choice of a suitable penalty often determining the reliability and interpretability of downstream solutions. While recent…