Month: January 2020

On the convexification of constrained quadratic optimization problems with indicator variables

  • Andrés Gómez
  • Simge Küçükyavuz
  • Linchuan Wei
    • Categories (Mixed) Integer Nonlinear Programming, Quadratic Programming Tags , , , ,

    Motivated by modern regression applications, in this paper, we study the convexification of quadratic optimization problems with indicator variables and combinatorial constraints on the indicators. Unlike most of the previous work on convexification of sparse regression problems, we simultaneously consider the nonlinear objective, indicator variables, and combinatorial constraints. We prove that for a separable quadratic … Read more

    Substitution-based Equipment Balancing in Service Networks with Multiple Equipment Types

  • Natashia Boland
  • Alan L. Erera
  • Martin Savelsbergh
  • Yassine Ridouane
  • Yu Yang
    • Categories Applications - OR and Management Sciences, Transportation

    We investigate substitution-based equipment balancing for a package express carrier operating multiple equipment types in its service network. The weekly schedule of movements used to transport packages through the service network leads to changes in equipment inventory at the facilities in the network. We seek to reduce this change, i.e., the equipment imbalance associated with … Read more

    Proximal splitting algorithms: Relax them all!

  • Laurent Condat
  • Andres Contreras
  • Akira Hirabayashi
  • Daichi Kitahara
    • Categories Nonlinear Optimization, Nonsmooth Optimization

    Convex optimization problems, whose solutions live in very high dimensional spaces, have become ubiquitous. To solve them, proximal splitting algorithms are particularly adequate: they consist of simple operations, by handling the terms in the objective function separately. We present several existing proximal splitting algorithms and we derive new ones, within a unified framework, which consists … Read more

    A parallel splitting ALM-based algorithm for separable convex programming

  • Bingsheng He
  • Shengjie Xu
    • Categories Convex and Nonsmooth Optimization, Convex Optimization, Parallel Algorithms Tags , , , ,

    The augmented Lagrangian method (ALM) provides a benchmark for tackling the canonical convex minimization problem with linear constraints. We consider a special case where the objective function is the sum of $m$ individual subfunctions without coupled variables. The recent study reveals that the direct extension of ALM for separable convex programming problems is not necessarily … Read more

    On pricing-based equilibrium for network expansion planning. A multi-period bilevel approach under uncertainty

  • Laureano F. Escudero
  • Antonio M. Rodríguez-Chía
  • Juan F. Monge
    • Categories Applications - OR and Management Sciences

    This study focuses on the development of a mixed binary primal-dual bilinear model for multi-period bilevel network expansion planning under uncertainty, where pricing-based equilibrated strategic and operational decisions are to be made. The periodwise dependent parameters’ uncertainty is represented by a _nite set of scenarios. Pricing-based equilibrium is required in the models to be optimized … Read more

    Robust location-transportation problems with integer-valued demand

  • Ahmadreza Marandi
  • Geert-Jan van Houtum
    • Categories Applications - OR and Management Sciences, Network Optimization, Robust Optimization Tags , , ,

    A Location-Transportation (LT) problem concerns designing a company’s distribution network consisting of one central warehouse with ample stock and multiple local warehouses for a long but finite time horizon. The network is designed to satisfy the demands of geographically dispersed customers for multiple items within given delivery time targets. The company needs to decide on … Read more

    On the acceleration of the Barzilai-Borwein method

  • Yu-Hong Dai
  • Yakui Huang
  • Xin-Wei Liu
  • Hongchao Zhang
    • Categories Convex and Nonsmooth Optimization, Nonlinear Optimization

    The Barzilai-Borwein (BB) gradient method is efficient for solving large-scale unconstrained problems to the modest accuracy and has a great advantage of being easily extended to solve a wide class of constrained optimization problems. In this paper, we propose a new stepsize to accelerate the BB method by requiring finite termination for minimizing two-dimensional strongly … Read more

    Dynamic programming for the time-dependent traveling salesman problem with time windows

  • Gonzalo Lera-Romero
  • Juan José Miranda-Bront
  • Francisco J. Soulignac
    • Categories Dynamic Programming, Transportation Tags , , , , ,

    The recent growth of direct-to-consumer deliveries has stressed the importance of last-mile logistics, becoming one of the critical factors in city planning. One of the key factors lies in the last-mile deliveries, reaching in some cases nearly 50% of the overall parcel delivery cost. Different variants of the the well-known Traveling Salesman Problem (TSP) arise … Read more

    A Regularized Smoothing Method for Fully Parameterized Convex Problems with Applications to Convex and Nonconvex Two-Stage Stochastic Programming

  • Pedro Borges de Melo
  • Claudia Sagastizábal
  • Mikhail V. Solodov
    • Categories Nonlinear Optimization, Nonsmooth Optimization, Stochastic Programming Tags , , , , ,

    We present an approach to regularize and approximate solution mappings of parametric convex optimization problems that combines interior penalty (log-barrier) solutions with Tikhonov regularization. Because the regularized mappings are single-valued and smooth under reasonable conditions, they can be used to build a computationally practical smoothing for the associated optimal value function. The value function in … Read more

    Risk-Neutral and Risk-Averse Transmission Switching for Load Shed Recovery

  • Manish Bansal
  • Adolfo Escobedo
  • Yingqiu Zhang
    • Categories Applications - OR and Management Sciences, Energy, Stochastic Programming Tags , , ,

    Maintaining an uninterrupted supply of electricity is a fundamental goal of power systems operators. However, due to critical outage events, customer demand or load is at times disconnected or shed temporarily. While deterministic optimization models have been devised to help operators expedite load shed recovery by harnessing the flexibility of the grid’s topology (i.e., transmission … Read more