An explicit Tikhonov algorithm for nested variational inequalities

  • Lorenzo Lampariello
  • Christoph Neumann
  • Simone Sagratella
  • Oliver Stein
  • Jacopo Maria Ricci
    • Categories Complementarity and Variational Inequalities, Convex Optimization

    We consider nested variational inequalities consisting in a (upper-level) variational inequality whose feasible set is given by the solution set of another (lower-level) variational inequality. Purely hierarchical convex bilevel optimization problems and certain multi-follower games are particular instances of nested variational inequalities. We present an explicit and ready-to-implement Tikhonov-type solution method for such problems. We … Read more

    Implicit steepest descent algorithm for optimization with orthogonality constraints

  • Harry Oviedo
    • Categories Nonlinear Optimization

    Optimization with orthogonality constraints problems appear widely in applications from science and engineering. We address these types of problems from an numerical approach. Our new framework combines the steepest gradient descent using implicit information with and operator projection in order to construct a feasible sequence of points. In addition, we adopt an adaptive Barzilai–Borwein steplength … Read more

    Strong Relaxations for Continuous Nonlinear Programs Based on Decision Diagrams

  • Danial Davarnia
    • Categories (Mixed) Integer Nonlinear Programming, Cutting Plane Approaches, Global Optimization

    Over the past decade, Decision Diagrams (DDs) have risen as a powerful modeling tool to solve discrete optimization problems. The extension of this emerging concept to continuous problems, however, has remained a challenge, posing a limitation on its applicability scope. In this paper, we introduce a novel framework that utilizes DDs to model continuous programs. … Read more

    Orbital Conflict: Cutting Planes for Symmetric Integer Programs

  • Jeff Linderoth
  • James Ostrowski
  • Jose Nunez-Ares
  • Fabrizio Rossi
  • Stefano Smriglio
    • Categories Branch and Cut Algorithms, Integer Programming Tags

    Cutting planes have been an important factor in the impressive progress made by integer programming (IP) solvers in the past two decades. However, cutting planes have had little impact on improving performance for symmetric IPs. Rather, the main breakthroughs for solving symmetric IPs have been achieved by cleverly exploiting symmetry in the enumeration phase of … Read more

    A Combinatorial Cut-and-Lift Procedure with an Application to 0-1 Chance Constraints

  • J. Christopher Beck
  • Margarita P Castro
  • Andre Augusto Cire
    • Categories 0-1 Programming, Cutting Plane Approaches, Second-Order Cone Programming Tags , , ,

    Cut generation and lifting are key components for the performance of state-of-the-art mathematical programming solvers. This work proposes a new general cut-and-lift procedure that exploits the combinatorial structure of 0-1 problems via a binary decision diagram (BDD) encoding of their constraints. We present a general framework that can be applied to a large range of … Read more

    Optimal Power Flow in Distribution Networks under N-1 Disruptions: A Multi-stage Stochastic Programming Approach

  • Harsha Nagarajan
  • Haoxiang Yang
    • Categories Stochastic Programming Tags , , , ,

    Contingency research to find optimal operations and post-contingency recovery plans in distribution networks has gained a major attention in recent years. To this end, we consider a multi-period optimal power flow (OPF) problem in distribution networks, subject to the N-1 contingency where a line or distributed energy resource fails. The contingency can be modeled as … Read more

    Improving solve times of stable matching problems through preprocessing

  • Maxence Delorme
  • Jacek Gondzio
  • William Pettersson
  • Sergio García
  • Joerg Kalcsics
  • David Manlove
    • Categories Combinatorial Optimization, Integer Programming, Optimization Software Benchmark Tags , , ,

    We present new theory, heuristics and algorithms for preprocessing instances of the Stable Marriage with Ties and Incomplete lists (SMTI), the Hospitals/Residents with Ties (HRT), and the Worker-Firms with Ties (WFT) problems. We show that instances of these problems can be preprocessed by removing from the preference lists of some agents entries that correspond to … Read more

    Effectively managing diagnostic tests to monitor the COVID-19 outbreak in Italy

  • Lorenzo Lampariello
  • Simone Sagratella
    • Categories Biomedical Applications, Convex Optimization

    Urged by the outbreak of the COVID-19 in Italy, this study aims at helping to tackle the spread of the disease by resorting to operations research techniques. In particular, we propose a mathematical program to model the problem of establishing how many diagnostic tests the Italian regions must perform in order to maximize the overall … Read more

    Practical Risk Modeling for the Stochastic Technician Routing and Scheduling Problem

  • Luke Marshall
  • Timur Tankayev
    • Categories Applications - OR and Management Sciences, Stochastic Programming

    Planning for uncertainty is crucial for finding good, stable solutions. However, it is often impractical to incorporate stochastic elements into a large production system. Our paper tackles this issue in the context of the Technician Routing and Scheduling Problem (TRSP). We develop a set of techniques, based on phase-type distributions, to quickly and accurately evaluate … Read more

    Service Network Design for Same-Day Delivery with Hub Capacity Constraints

  • Haotian Wu
  • Ian Herszterg
  • Martin Savelsbergh
  • Yixiao Huang
    • Categories Applications - OR and Management Sciences, Transportation Tags , , ,

    We study a new service network design problem for an urban same-day delivery system in which the number of vehicles that can simultaneously load or unload at a hub is limited. Due to the presence of both time constraints for the commodities and capacity constraints at the hubs, it is no longer guaranteed that a … Read more