We analyze the problem of identifying large cliques in graphs that are affected by adversarial uncertainty. More specifically, we consider a new formulation, namely the adversarial maximum clique problem, which extends the classical maximum-clique problem to graphs with edges strategically perturbed by an adversary. The proposed mathematical model is thus formulated as a two-player zero-sum … Read more
In this paper, we propose a new acceleration strategy for gradient-based methods applied to strictly convex Quadratic Programming (QP) problems. The strategy consists in performing, at selected iterations, minimization steps along alternative descent directions or even within low-dimensional affine subspaces. In particular, considering the contribution of the linear and quadratic part of the objective function … Read more
Convex maximization arises in many applications but is generally NP-hard, even for low-rank objectives. This paper introduces a set of broadly applicable conditions that certify when such problems are polynomially solvable. Our main condition is a new property of the feasible set, which we term co-monotonicity. We show that this property holds for two important … Read more
We introduce method iR2N, a modified proximal quasi-Newton method for minimizing the sum of a \(C^1\) function \(f\) and a lower semi-continuous prox-bounded \(h\) that permits inexact evaluations of \(f\), \(\nabla f\) and of the relevant proximal operators. Both \(f\) and \(h\) may be nonconvex. In applications where the proximal operator of \(h\) is not … Read more
This paper addresses an operational planning challenge in two-tier robotized sorting systems (T-RSS), an emerging alternative to traditional conveyor-based sorting in e-commerce delivery stations. Designed to be compact and space-efficient, T-RSS use an upper tier to sort parcels from loading stations to drop-off points, which connect to roll containers on a lower tier where parcels … Read more
When optimizing a nonlinear objective, one can employ a neural network as a surrogate for the nonlinear function. However, the resulting optimization model can be time-consuming to solve globally with exact methods. As a result, local search that exploits the neural-network structure has been employed to find good solutions within a reasonable time limit. For … Read more
The tractability of optimization problems depends critically on structural properties of the objective function. Convexity guarantees global optimality of local solutions and enables polynomial-time algorithms under mild assumptions, but many problems arising in modern applications—particularly in machine learning—are inherently nonconvex. Remarkably, a large class of such problems remains amenable to efficient optimization due to additional … Read more
This paper proposes a unified framework for designing robustness in optimization under uncertainty using gauge sets, convex sets that generalize distance and capture how distributions may deviate from a nominal reference. Representing robustness through a gauge set reweighting formulation brings many classical robustness paradigms under a single convex-analytic perspective. The corresponding dual problem, the upper … Read more
Capacity Planning problems are a class of optimization problems used in diverse industries to improve resource allocation and make investment decisions. Solving real-world instances of these problems typically requires significant computational effort. To tackle this, we propose machine-learning-aided column generation methods for solving large-scale capacity planning problems. Our goal is to accelerate column generation by … Read more
This paper surveys optimization problems arising in agriculture, energy systems, and water-energy coordination from an operations research perspective. These problems are commonly formulated as integer nonlinear programs, mixed-integer nonlinear programs, or combinatorial set optimization models, characterized by nonlinear physical constraints, discrete decisions, and intertemporal coupling. Such structures pose significant computational challenges in large-scale and repeated-solution … Read more