We study the minimization of a rank-one quadratic with indicators and show that the underlying set function obtained by projecting out the continuous variables is supermodular. Although supermodular minimization is, in general, difficult, the specific set function for the rank-one quadratic can be minimized in linear time. We show that the convex hull of the … Read more
We study the linked tactical design problems of fleet sizing and partitioning a service region into vehicle routing zones for same-day delivery (SDD) systems. Existing SDD studies focus primarily on operational dispatch problems and do not consider system design questions. Prior work on SDD system design has not considered the fleet sizing decision when a … Read more
Minimax optimization has become a central tool for modern machine learning with applications in generative adversarial networks, robust optimization, reinforcement learning, etc. These applications are often nonconvex-nonconcave, but the existing theory is unable to identify and deal with the fundamental difficulties posed by nonconvex-nonconcave structures. In this paper, we study the classic proximal point method … Read more
A binary constraint satisfaction problem (BCSP) consist in determining an assignment of values to variables which is compatible with a set of constraints. The problem is called binary because the constraints involve only pairs of variables. The BCSP is a cornerstone problem in Constraint Programming (CP), appearing in a very wide range of real-world applications. … Read more
We construct a general framework for deriving error bounds for conic feasibility problems. In particular, our approach allows one to work with cones that fail to be amenable or even to have computable projections, two previously challenging barriers. For the purpose, we first show how error bounds may be constructed using objects called one-step facial … Read more
Sequential Residual Methods try to solve nonlinear systems of equations $F(x)=0$ by iteratively updating the current approximate solution along a residual-related direction. Therefore, memory requirements are minimal and, consequently, these methods are attractive for solving large-scale nonlinear systems. However, the convergence of these algorithms may be slow in critical cases; therefore, acceleration procedures are welcome. … Read more
A Discrete-Time Linear Complementarity System (DLCS) is a dynamical system in discrete time whose state evolution is governed by linear dynamics in states and algebraic variables that solve a Linear Complementarity Problem (LCP). A DLCS is the hybrid dynamical system that is the discrete-time counterpart of the well-known Linear Complementarity System (LCS). We derive sufficient … Read more
Due to different disasters, natural or men made, world is facing the problem of massive damage of life and property. To save the life of maximum number of evacuees, an efficient evacuation planning is essential. Prioritization is the process of deciding the relative importance or urgency of things or objects. It helps to focus on … Read more
Optimization with stochastic dominance constraints has recently received an increasing amount of attention in the quantitative risk management literature. Instead of requiring that the probabilistic description of the uncertain parameters be exactly known, this paper presents the first comprehensive study of a data-driven formulation of the distributionally robust second-order stochastic dominance constrained problem (DRSSDCP) that … Read more
In real-time traffic management, a new schedule for the vehicles must be computed whenever a deviation from the current plan is detected, or periodically after some time. If this time interval is relatively small, then each two consecutive instances are likely to be similar. We exploit this aspect to derive an exact reoptimization framework for … Read more