Wasserstein Logistic Regression with Mixed Features

Recent work has leveraged the popular distributionally robust optimization paradigm to combat overfitting in classical logistic regression. While the resulting classification scheme displays a promising performance in numerical experiments, it is inherently limited to numerical features. In this paper, we show that distributionally robust logistic regression with mixed (i.e., numerical and categorical) features, despite amounting … Read more

Complexity-Optimal and Curvature-Free First-Order Methods for Finding Stationary Points of Composite Optimization Problems

This paper develops and analyzes an accelerated proximal descent method for finding stationary points of nonconvex composite optimization problems. The objective function is of the form f+h where h is a proper closed convex function, f is a differentiable function on the domain of h, and the gradient of f is Lipschitz continuous on the … Read more

Neur2SP: Neural Two-stage Stochastic Programming

Stochastic programming is a powerful modeling framework for decision-making under uncertainty. In this work, we tackle two-stage stochastic programs (2SPs), the most widely applied and studied class of stochastic programming models. Solving 2SPs exactly requires evaluation of an expected value function that is computationally intractable. Additionally, having a mixed-integer linear program (MIP) or a nonlinear … Read more

A Reduced Jacobian Scheme with Full Convergence for Multicriteria Optimization

In this paper, we propose a variant of the reduced Jacobian method (RJM) introduced by El Maghri and Elboulqe in [JOTA, 179 (2018) 917–943] for multicriteria optimization under linear constraints. Motivation is that, contrarily to RJM which has only global convergence to Pareto KKT-stationary points in the classical sense of accumulation points, this new variant … Read more

Accelerating Frank-Wolfe via Averaging Step Directions

The Frank-Wolfe method is a popular method in sparse constrained optimization, due to its fast per-iteration complexity. However, the tradeoff is that its worst case global convergence is comparatively slow, and importantly, is fundamentally slower than its flow rate–that is to say, the convergence rate is throttled by discretization error. In this work, we consider … Read more

On complexity constants of linear and quadratic models for derivative-free trust-region algorithms

Complexity analysis has become an important tool in the convergence analysis of optimization algorithms. For derivative-free optimization algorithms, it is not different. Interestingly, several constants that appear when developing complexity results hide the dimensions of the problem. This work organizes several results in literature about bounds that appear in derivative-free trust-region algorithms based on linear … Read more

A Constraint Dissolving Approach for Nonsmooth Optimization over the Stiefel Manifold

This paper focus on the minimization of a possibly nonsmooth objective function over the Stiefel manifold. The existing approaches either lack efficiency or can only tackle prox-friendly objective functions. We propose a constraint dissolving function named NCDF and show that it has the same first-order stationary points and local minimizers as the original problem in … Read more

A Ramsey-Type Equilibrium Model with Spatially Dispersed Agents

We present a spatial and time-continuous Ramsey-type equilibrium model for households and firms that interact on a spatial domain to model labor mobility in the presence of commuting costs. After discretization in space and time, we obtain a mixed complementarity problem that represents the spatial equilibrium model. We prove existence of equilibria using the theory … Read more

Conditional Distributionally Robust Functionals

Risk measures incorporate a conservative or risk averse perspective in decisionmaking under uncertainty. Taking a variety of models for the potential outcomes into account, the distributionally robust decision is the most conservative decision among the decisions available. This paper investigates different versions of conditional risk measures and distributionally robust functionals in a multistage setting. The … Read more

Logic-based Benders decomposition with a partial assignment acceleration technique for avionics scheduling

Pre-runtime scheduling of large-scale electronic systems, as those in modern aircraft, can be computationally challenging. In this paper, we study a distributed integrated modular avionic system of practical relevance where the scheduling includes to assign communication messages to time slots and to sequence tasks on modules. For this problem, the challenge is the huge number … Read more