We theoretically and computationally compare the strength of the three main upper bounds from the literature on the optimal value of the Edge-Weighted Maximum Clique Problem (EWMCP). We provide a set of instances for which the ratio between any of the three upper bounds and the optimal value of the EWMCP is unbounded, showing that … Read more
This paper presents scalable algorithms for computing pure Nash equilibria (PNEs) in large-scale integer programming games (IPGs), where existing exact methods typically handle only small numbers of players. Motivated by a county-level aquatic invasive species (AIS) prevention problem with 84 decision makers, we develop and analyze random-restart best-response dynamics (RR-BRD), a randomized search framework for … Read more
Bilevel optimization problems arise in numerous real-world applications. While single-level reformulations are a common strategy for solving convex bilevel problems, such approaches usually fail when the follower’s problem includes integer variables. In this paper, we present the first single-level reformulation for mixed-integer linear bilevel optimization, which does not rely on the follower’s value function. Our … Read more
This paper introduces a novel algorithm for Mixed-Integer Nonlinear Programming (MINLP) problems with multilinear interpolations of look-up tables. These problems arise when objectives or constraints contain black-box functions only known at a finite set of evaluations on a predefined grid. We derive a piecewise-linear relaxation for the multilinear interpolants, which require an MINLP formulation. Supported … Read more
When linear dependence exists between some explanatory variables in a regression model, the estimates of regression coefficients become unstable, thereby making the interpretation of the estimation results unreliable. To eliminate such multicollinearity, we propose a high-performance method for selecting the best subset of explanatory variables for linear and logistic regression models. Specifically, we first derive … Read more
We consider Nash equilibrium problems with mixed-integer variables in which each player solves a mixed-integer optimization problem parameterized in the rivals’ strategies. We distinguish between standard Nash equilibrium problems (NEP), where the parameterization acts only on the players’ cost functions and generalized Nash equilibrium problems (GNEPs), where, additionally, the strategy spaces of the players may … Read more
We consider mixed-integer linear chance-constrained problems for which the random vector that parameterizes the feasible region has finite support. Our key objective is to improve branch-and-bound or -cut approaches by introducing new types of valid inequalities that improve the dual bound and, by this, the overall performance of such methods. We introduce so-called multi-disjunctive valid … Read more
Logistic regression models are widely used in the social and behavioral sciences and in high-stakes domains, due to their simplicity and interpretability properties. At the same time, such domains are permeated by distribution shifts, where the distribution generating the data changes between training and deployment. In this paper, we study a distributionally robust logistic regression … Read more
We study inverse optimization (IO), where the goal is to use a parametric optimization program as the hypothesis class to infer relationships between input-decision pairs. Most of the literature focuses on learning only the objective function, as learning the constraint function (i.e., feasible regions) leads to nonconvex training programs. Motivated by this, we focus on … Read more
Since the inception of ISOs, Locational Marginal Prices (LMPs) alone were not market clearing or incentive compatible because an auction winner who offered its avoidable costs could lose money at the LMPs. ISOs used make-whole payments to ensure that market participants did not lose money. Make-whole payments were not public, creating transparency issues. Over time, … Read more