On inexact relative-error hybrid proximal extragradient, forward-backward and Tseng’s modified forward-backward methods with inertial effects

  • M. Marques Alves
  • Raul T. Marcavillaca
    • Categories Convex and Nonsmooth Optimization Tags , , , , , , , ,

    In this paper, we propose and study the asymptotic convergence and nonasymptotic global convergence rates (iteration-complexity) of an inertial under-relaxed version of the relative-error hybrid proximal extragradient (HPE) method for solving monotone inclusion problems. We analyze the proposed method under more flexible assumptions than existing ones on the extrapolation and relative-error parameters. As applications, we … Read more

    Convergence of Finite-Dimensional Approximations for Mixed-Integer Optimization with Differential Equations

  • Falk M. Hante
  • Martin Schmidt
    • Categories (Mixed) Integer Nonlinear Programming, Nonlinear Optimization, Systems governed by Differential Equations Optimization Tags , , , ,

    We consider a direct approach to solve mixed-integer nonlinear optimization problems with constraints depending on initial and terminal conditions of an ordinary differential equation. In order to obtain a finite-dimensional problem, the dynamics are approximated using discretization methods. In the framework of general one-step methods, we provide sufficient conditions for the convergence of this approach … Read more

    A New Extended Formulation with Valid Inequalities for the Capacitated Concentrator Location Problem

  • Massimo Di Francesco
  • Manlio Gaudioso
  • Enrico Gorgone
  • Ishwar Murthy
    • Categories Branch and Cut Algorithms, Transportation Tags , ,

    In this paper, we first present a new extended formulation of the Capacitated Concentrator Location Problem (CCLP) using the notion of cardinality of terminals assigned to a concentrator location. The disaggregated formulation consists of O(mn2) variables and constraints, where m denotes the number of concentrators and n the number of terminals. An immediate benefit of … Read more

    The Sard theorem for essentially smooth locally Lipschitz maps and applications in optimization

  • Xuan Duc Ha Truong
    • Categories Convex and Nonsmooth Optimization, Multi-Criteria Optimization Tags , , , ,

    The classical Sard theorem states that the set of critical values of a $C^{k}$-map from an open set of $\R^n$ to $\R^p$ ($n\geq p$) has Lebesgue measure zero provided $k\geq n-p+1$. In the recent paper by Barbet, Dambrine, Daniilidis and Rifford, the so called “preparatory Sard theorem” for a compact countable set $I$ of $C^k$ … Read more

    Policies for Inventory Models with Product Returns Forecast from Past Demands and Past Sales

  • Mabel C. Chou
  • Chee-Khian Sim
  • Xiao-Ming Yuan
    • Categories Dynamic Programming, Supply Chain Management

    Finite horizon periodic review backlog models are considered in this paper for an inventory system that remanufactures two types of cores: buyback cores and normal cores. Returns of used products as buyback cores are modelled to depend on past demands and past sales. We obtain an optimal inventory policy for the model in which returns … Read more

    Group sparse recovery in impulsive noise via alternating direction method of multipliers

  • Jianjun Wang
  • Jianwen Huang
  • Wang Wendong
  • Feng Zhang
    • Categories Applications - Science and Engineering, Control Applications, Data-Mining

    In this paper, we consider the recovery of group sparse signals corrupted by impulsive noise. In some recent literature, researchers have utilized stable data fitting models, like $l_1$-norm, Huber penalty function and Lorentzian-norm, to substitute the $l_2$-norm data fidelity model to obtain more robust performance. In this paper, a stable model is developed, which exploits … Read more

    A New Face Method for Linear Programming

  • Ping-Qi Pan
    • Categories Linear Programming Tags , , , ,

    An attractive feature of the face method \cite{pan14} for solving LP problems is that it uses the orthogonal projection of the negative objective gradient on the related null space as the search direction. However, the method would not be amenable for solving large sparse problems, since it handles the involved normal system by orthogonal transformations. … Read more

    Stochastic Hydro-thermal Unit Commitment via Multi-level Scenario Trees and Bundle Regularization

  • Vitor de Matos
  • Claudia Sagastizábal
  • Erlon Finardi
  • R. D. Lobato
  • Asgeir Tomasgard
    • Categories Nonlinear Optimization, Stochastic Programming

    For an electric power mix subject to uncertainty, the stochastic unit-commitment problem finds short-term optimal generation schedules that satisfy several system-wide constraints. In regulated electricity markets, this very practical and important problem is used by the system operator to decide when each unit is to be started or stopped, and to define how to generate … Read more

    A dual spectral projected gradient method for log-determinant semidefinite problems

  • Mituhiro Fukuda
  • Sunyoung Kim
  • Takashi Nakagaki
  • Makoto Yamashita
    • Categories Convex Optimization, Semi-definite Programming Tags , , , ,

    We extend the result on the spectral projected gradient method by Birgin et al in 2000 to a log-determinant semidefinite problem (SDP) with linear constraints and propose a spectral projected gradient method for the dual problem. Our method is based on alternate projections on the intersection of two convex sets, which first projects onto the … Read more

    On prime and minimal representations of a face of a polyhedron

  • Ta Van Van Tu
    • Categories Combinatorial Optimization, Multi-Criteria Optimization, Polyhedra

    In this paper, a new method for determining all minimal representations of a face of a polyhedron is proposed. A main difficulty for determining prime and minimal representations of a face is that the deletion of one redundant constraint can change the redundancy of other constraints. To reduce computational efforts in finding all minimal representations … Read more