A family of optimal weighted conjugate-gradient-type methods for strictly convex quadratic minimization

  • Roberto Andreani
  • Harry Oviedo
  • Marcos Raydan
    • Categories Unconstrained Optimization Tags , , , ,

    We introduce a family of weighted conjugate-gradient-type methods, for strictly convex quadratic functions, whose parameters are determined by a minimization model based on a convex combination of the objective function and its gradient norm. This family includes the classical linear conjugate gradient method and the recently published delayed weighted gradient method as the extreme cases … Read more

    Short-Term Inventory-Aware Equipment Management in Service Networks

  • Natashia Boland
  • Alan L. Erera
  • Martin Savelsbergh
  • Yassine Ridouane
    • Categories (Mixed) Integer Linear Programming, Production and Logistics, Transportation

    Logistics companies often operate a heterogeneous fleet of equipment to support their service network operations. This introduces a layer of planning complexity as facilities need to maintain appropriate levels of equipment types to support operations throughout the planning horizon. We formulate an optimization model that minimizes the cost of executing a load plan, assuming knowledge … Read more

    Strengthened SDP Relaxation for an Extended Trust Region Subproblem with an Application to Optimal Power Flow

  • Samuel Burer
  • Anders Eltved
    • Categories Quadratic Programming, Semi-definite Programming Tags ,

    We study an extended trust region subproblem minimizing a nonconvex function over the hollow ball $r \le \|x\| \le R$ intersected with a full-dimensional second order cone (SOC) constraint of the form $\|x – c\| \le b^T x – a$. In particular, we present a class of valid cuts that improve existing semidefinite programming (SDP) … Read more

    A Branch-and-Price Algorithm Enhanced by Decision Diagrams for the Kidney Exchange Problem

  • Dionne M. Aleman
  • Merve Bodur
  • Lizeth Carolina Riascos-Alvarez
    • Categories Integer Programming

    Kidney paired donation programs allow patients registered with an incompatible donor to receive a suitable kidney from another donor, as long as the latter’s co-registered patient, if any, also receives a kidney from a different donor. The kidney exchange problem (KEP) aims to find an optimal collection of kidney exchanges taking the form of cycles … Read more

    Bicriteria approaches for an optimal balance between resilience and cost-effectiveness of supply chains

  • Heiner Ackermann
  • Erik Diessel
    • Categories Multi-Criteria Optimization, Supply Chain Management Tags , , ,

    In supply chain optimization multiple objectives are considered simultaneously, for example to increase resilience and reduce costs. In this paper we discuss the corresponding bicriteria problems to find a good balance between these two objectives. We give a general model for supply chain resilience that integrates strategic decisions with the operational level. This modular model … Read more

    Global optimality in minimum compliance topology optimization of frames and shells by moment-sum-of-squares hierarchy

  • Didier Henrion
  • Martin Kružík
  • Marek Tyburec
  • Jan Zeman
    • Categories Civil and Environmental Engineering, Constrained Nonlinear Optimization, Semi-definite Programming Tags , , , , ,

    The design of minimum-compliance bending-resistant structures with continuous cross-section parameters is a challenging task because of its inherent non-convexity. Our contribution develops a strategy that facilitates computing all guaranteed globally optimal solutions for frame and shell structures under multiple load cases and self-weight. To this purpose, we exploit the fact that the stiffness matrix is … Read more

    Precise control of approximation quality in multicriteria optimization

  • Erik Diessel
    • Categories Multi-Criteria Optimization Tags , , ,

    Although many algorithms for multicriteria optimization provide good approximations, a precise control of their quality is challenging. In this paper we provide algorithmic tools to obtain exact approximation quality values for given approximations and develop a new method for multicriteria optimization guided by this quality. We show that the well-established “-indicator measure is NP-hard to … Read more

    The Bipartite Boolean Quadric Polytope with Multiple-Choice Constraints

  • Andreas Bärmann
  • Alexander Martin
  • Oskar Schneider
    • Categories (Mixed) Integer Nonlinear Programming, Chemical Engineering, Polyhedra Tags , , , ,

    We consider the bipartite boolean quadric polytope (BQP) with multiple-choice constraints and analyse its combinatorial properties. The well-studied BQP is defined as the convex hull of all quadric incidence vectors over a bipartite graph. In this work, we study the case where there is a partition on one of the two bipartite node sets such … Read more

    Are Weaker Stationarity Concepts of Stochastic MPCC Problems Significant in Absence of SMPCC-LICQ?

  • Arnab Sur
    • Categories Stochastic Programming Tags , , , ,

    In this article, we study weak stationarity conditions (A- and C-) for a particular class of degenerate stochastic mathematical programming problems with complementarity constraints (SMPCC, for short). Importance of the weak stationarity concepts in absence of SMPCC-LICQ are presented through toy problems in which the point of local or global minimum are weak stationary points … Read more

    Stokes, Gibbs and volume computation of semi-algebraic sets

  • Didier Henrion
  • Jean-Bernard Lasserre
  • Matteo Tacchi
    • Categories Infinite Dimensional Optimization, Semi-definite Programming Tags , ,

    We consider the problem of computing the Lebesgue volume of compact basic semi-algebraic sets. In full generality, it can be approximated as closely as desired by a converging hierarchy of upper bounds obtained by applying the Moment-SOS (sums of squares) methodology to a certain infinite-dimensional linear program (LP). At each step one solves a semidefinite … Read more