We propose a novel approach to modeling fairness in the Vehicle Routing Problem (VRP) by introducing objective functions based on ordering route lengths, capturing both monotonic and non-monotonic equity measures. Our method ensures allocations that are efficient, capacity-feasible, and equitable according to criteria like min-max, range, Gini, variance, or absolute deviations. To prevent biased or … Read more
Decision-dependent robust optimization (DDRO) problems are usually tackled by reformulating them using a strong-duality theorem for the uncertainty set model. If the uncertainty set is, however, described by a mixed-integer linear model, dualization techniques cannot be applied and the literature on solution methods is very scarce. In this paper, we exploit the equivalence of DDRO … Read more
In this manuscript, we introduce a novel projected gradient algorithm for solving quasiconvex optimization problems over closed convex sets. The key innovation of our new algorithm is an adaptive, parameter-free stepsize rule that requires no line search and avoids estimating constants, such as Lipschitz modulus. Unlike recent self-adaptive approach given in [17] which typically produce … Read more
Extreme weather events, like flooding, disrupt urban transportation networks by reducing speeds and capacities, and by closing roadways. These hazards create regime-dependent uncertainty in link performance and travel-time distribution tails, challenging conventional traffic assignment that relies on the expectation of cost or mean excess of cost summation. This study develops a risk- and ambiguity-aware traffic … Read more
This paper develops negative curvature methods for continuous nonlinear unconstrained optimization in stochastic settings, in which function, gradient, and Hessian information is available only through probabilistic oracles, i.e., oracles that return approximations of a certain accuracy and reliability. We introduce conditions on these oracles and design a two-step framework that systematically combines gradient and negative … Read more
In this paper, we compare the strength of alternate formulations (polyhedra) of the binary knapsack set. We introduce a specific class of knapsack sets for which we prove that the polyhedra based on their minimal cover inequalities (together with the bounds on the variables) are strictly contained inside the polyhedra defined by their continuous knapsack … Read more
We study linear complementarity problems (LCPs) under uncertainty, which we model using chance constraints. Since the complementarity condition of the LCP is an equality constraint, it is required to consider relaxations, which naturally leads to optimization problems in which the relaxation parameters are minimized for given probability levels. We focus on these optimization problems and … Read more
This paper studies convex quadratic minimization problems in which each continuous variable is coupled with a binary indicator variable. We focus on the structured setting where the Hessian matrix of the quadratic term is positive definite and exhibits sparsity. We develop an exact parametric dynamic programming algorithm whose computational complexity depends explicitly on the treewidth … Read more
We present an effective warm-starting scheme for solving large linear complementarity problems (LCPs) arising from Nash equilibrium problems. The approach generates high-quality starting points that, when passed to the PATH solver, yield substantial reductions in computational time and variance. Our warm-start routine reformulates each agent’s LP using strong duality, leading to a master problem with … Read more
Quasinormality is a classical constraint qualification originally introduced by Hestenes in 1975 and subsequently extensively studied in nonlinear programming and in problems with abstract constraints. In this paper, we extend this concept to the setting of nonlinear semidefinite programming (NSDP). We show that the proposed condition is strictly weaker than Robinson’s constraint qualification, while still … Read more