Iteration complexity analysis of a partial LQP-based alternating direction method of multipliers

  • Jianchao Bai
  • Yuxue Ma
  • Hao Sun
  • Miao Zhang
    • Categories Convex Optimization, Global Optimization Theory

    In this paper, we consider a prototypical convex optimization problem with multi-block variables and separable structures. By adding the Logarithmic Quadratic Proximal (LQP) regularizer with suitable proximal parameter to each of the first grouped subproblems, we develop a partial LQP-based Alternating Direction Method of Multipliers (ADMM-LQP). The dual variable is updated twice with relatively larger … Read more

    Equipping Barzilai-Borwein method with two dimensional quadratic termination property

  • Yu-Hong Dai
  • Yakui Huang
  • Xin-Wei Liu
    • Categories Convex Optimization, Nonlinear Optimization Tags , , , , ,

    A new gradient stepsize is derived at the motivation of equipping the Barzilai-Borwein (BB) method with two dimensional quadratic termination property. A remarkable feature of the new stepsize is that its computation only depends on the BB stepsizes in previous iterations without the use of exact line searches and Hessian, and hence it can easily … Read more

    An Inertial Block Majorization Minimization Framework for Nonsmooth Nonconvex Optimization

  • Nicolas Gillis
  • Le Thi Khanh Hien
  • Duy Nhat Phan
    • Categories Constrained Nonlinear Optimization Tags , , , , ,

    In this paper, we introduce TITAN, a novel inerTial block majorIzation minimization framework for non-smooth non-convex opTimizAtioN problems. TITAN is a block coordinate method (BCM) that embeds inertial force to each majorization-minimization step of the block updates. The inertial force is obtained via an extrapolation operator that subsumes heavy-ball and Nesterov-type accelerations for block proximal … Read more

    On Linear Bilevel Optimization Problems with Complementarity-Constrained Lower Levels

  • Steven A. Gabriel
  • Martin Schmidt
  • Marina Leal
    • Categories Applications - OR and Management Sciences, Complementarity and Variational Inequalities Tags , , , , ,

    We consider a novel class of linear bilevel optimization models with a lower level that is a linear program with complementarity constraints (LPCC). We present different single-level reformulations depending on whether the linear complementarity problem (LCP) as part of the lower-level constraint set depends on the upper-level decisions or not as well as on whether … Read more

    A Novel Solution Methodology for Wasserstein-based Data-Driven Distributionally Robust Problems

  • Carlos Gamboa
  • Tito Homem-de-Mello
  • Alexandre Street
  • Davi Valladão
    • Categories Stochastic Programming Tags , ,

    Distributionally robust optimization (DRO) is a mathematical framework to incorporate ambiguity over the actual data-generating probability distribution. Data-driven DRO problems based on the Wasserstein distance are of particular interest for their sound mathematical properties. For right-hand-sided uncertainty, however, existing methods rely on dual vertex enumeration rendering the problem intractable in practical applications. In this context, … Read more

    New exact approaches for the combined cell layout problem and extensions of the multi-bay facility layout problem

  • Mirko Dahlbeck
  • Anja Fischer
  • Philipp Hungerländer
  • Kerstin Maier
    • Categories (Mixed) Integer Linear Programming, Facility Planning and Design Tags , , , ,

    In this paper we consider the Combined Cell Layout Problem (CCLP), the Multi-Bay Facility Layout Problem (MBFLP) and several generalizations of the MBFLP, which have wide applications, e.g., in factory planning, heavy manufacturing, semiconductor fabrication and arranging rooms in hospitals. Given a set of cells of type single-row or directed-circular and a set of one-dimensional … Read more

    Planning the City Operations of a Parcel Express Company

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

    We introduce an interesting and challenging routing and scheduling problem arising in the city operations of SF Express, a large package express carrier in China. Vehicles execute multiple trips during a planning horizon spanning multiple shifts, where a trip can involve deliveries only, pickups only, or deliveries followed by pickups. Complicating factors include split deliveries … Read more

    Why there is no need to use a big-M in linear bilevel optimization: A computational study of two ready-to-use approaches

  • Thomas Kleinert
  • Martin Schmidt
    • Categories (Mixed) Integer Linear Programming, Complementarity and Variational Inequalities, Cutting Plane Approaches Tags , , , , ,

    Linear bilevel optimization problems have gained increasing attention both in theory as well as in practical applications of Operations Research (OR) during the last years and decades. The latter is mainly due to the ability of this class of problems to model hierarchical decision processes. However, this ability makes bilevel problems also very hard to … Read more

    Minimization of L1 over L2 for sparse signal recovery with convergence guarantee

  • Tao Min
    • Categories Applications - OR and Management Sciences Tags , , , , ,

    The ratio of the $L_1$ and $L_2$ norms, denoted by $L_1/L_2$, becomes attractive due to its scale-invariant property when approximating the $L_0$ norm to promote sparsity. In this paper, we incorporate the $L_1/L_2$ formalism into an unconstrained model in order to deal with both noiseless and noisy observations. To design an efficient algorithm, we derive … Read more

    Partial Lasserre relaxation for sparse Max-Cut

  • Juan S. Campos
  • Panos Parpas
  • Ruth Misener
    • Categories Semi-definite Programming Tags , , ,

    A common approach to solve or find bounds of polynomial optimization problems like Max-Cut is to use the first level of the Lasserre hierarchy. Higher levels of the Lasserre hierarchy provide tighter bounds, but solving these relaxations is usually computationally intractable. We propose to strengthen the first level relaxation for sparse Max-Cut problems using constraints … Read more