Month: December 2018

A generalization of linearized alternating direction method of multipliers for solving two-block separable convex programming

  • Song Dunjiang
  • Zhao Pengjun
  • Chang Xiaokai
  • Liu Sanyang
    • Categories Convex and Nonsmooth Optimization

    The linearized alternating direction method of multipliers (ADMM), with indefinite proximal regularization, has been proved to be efficient for solving separable convex optimization subject to linear constraints. In this paper, we present a generalization of linearized ADMM (G-LADMM) to solve two-block separable convex minimization model, which linearizes all the subproblems by choosing a proper positive-definite … Read more

    Weighted Thresholding Homotopy Method for Sparsity Constrained Optimization

  • Jianli Chen
  • Wenxing Zhu
  • Huating Huang
  • Lanfan Jiang
    • Categories Integer Programming Tags , , ,

    Weighted or reweighted strategies have not been considered for sparsity constrained optimization. In this paper, we reformulate the sparsity constraint as an equivalent weighted l1-norm constraint in the sparsity constrained optimization problem. To solve the reformulated problem, we investigate the problem in the Lagrange dual framework, and prove that the strong duality property holds. Then … Read more

    Large-scale Influence Maximization via Maximal Covering Location

  • Evren Güney
  • Markus Leitner
  • Mario Ruthmair
  • Markus Sinnl
    • Categories Applications - OR and Management Sciences, Integer Programming, Stochastic Programming Tags , , ,

    Influence maximization aims at identifying a limited set of key individuals in a (social) network which spreads information based on some propagation model and maximizes the number of individuals reached. We show that influence maximization based on the probabilistic independent cascade model can be modeled as a stochastic maximal covering location problem. A reformulation based … Read more

    Deep Unfolding of a Proximal Interior Point Method for Image Restoration

  • Carla Bertocchi
  • Émilie Chouzenoux
  • Marie-Caroline Corbineau
  • Jean-Christophe Pesquet
  • Marco Prato
    • Categories Convex and Nonsmooth Optimization, Network Optimization, Robust Optimization Tags , , , , ,

    Variational methods are widely applied to ill-posed inverse problems for they have the ability to embed prior knowledge about the solution. However, the level of performance of these methods significantly depends on a set of parameters, which can be estimated through computationally expensive and time-consuming methods. In contrast, deep learning offers very generic and efficient … Read more

    Machine learning approach to chance-constrained problems: An algorithm based on the stochastic gradient descent

  • Lukáš Adam
  • Martin Branda
    • Categories Stochastic Programming Tags , , , , ,

    We consider chance-constrained problems with discrete random distribution. We aim for problems with a large number of scenarios. We propose a novel method based on the stochastic gradient descent method which performs updates of the decision variable based only on looking at a few scenarios. We modify it to handle the non-separable objective. A complexity … Read more

    A note on solving nonlinear optimization problems in variable precision

  • Serge Gratton
  • Philippe L. Toint
    • Categories Applications - Science and Engineering, Nonlinear Systems and Least-Squares, Unconstrained Optimization Tags ,

    This short note considers an efficient variant of the trust-region algorithm with dynamic accuracy proposed Carter (1993) and Conn, Gould and Toint (2000) as a tool for very high-performance computing, an area where it is critical to allow multi-precision computations for keeping the energy dissipation under control. Numerical experiments are presented indicating that the use … Read more

    Decomposition Methods for Solving Two-Stage Distributionally Robust Optimization Problems

  • Hailin Sun
  • Huifu Xu
  • Chen Yannan
    • Categories Robust Optimization, Stochastic Programming Tags , , , , ,

    Decomposition methods have been well studied for solving two-stage and multi-stage stochastic programming problems, see [29, 32, 33]. In this paper, we propose an algorithmic framework based on the fundamental ideas of the methods for solving two-stage minimax distributionally robust optimization (DRO) problems where the underlying random variables take a finite number of distinct values. … Read more

    Integrated Trajectory-Location-Routing for Rapid Humanitarian Deliveries using Unmanned Aerial Vehicles

  • Panagiotis Angeloudis
  • Jose Javier Escribano Macias
  • Washington Ochieng
    • Categories Applications - OR and Management Sciences Tags , ,

    Unmanned Aerial Vehicles have the potential to provide an economical solution to the challenges of post-disaster land-based relief operations. Beyond regulatory concerns, technical and particularly airspace integration limitations inhibit their deployment in practice. To address these issues and ensure uninterrupted optimal operations, we present a novel approach consisting of an integrated trajectory-location-routing algorithm that seeks … Read more

    Intersection cuts for factorable MINLP

  • Felipe Serrano
    • Categories (Mixed) Integer Nonlinear Programming, Global Optimization Tags , ,

    Given a factorable function f, we propose a procedure that constructs a concave underestimor of f that is tight at a given point. These underestimators can be used to generate intersection cuts. A peculiarity of these underestimators is that they do not rely on a bounded domain. We propose a strengthening procedure for the intersection … Read more

    Volumetric barrier decomposition algorithms for two-stage stochastic linear semi-infinite programming

  • Lewa' Alzaleq
  • Baha Alzalg
  • Asma Gafour
    • Categories Linear Programming, Semi-infinite Programming, Stochastic Programming Tags , , , ,

    In this paper, we study the two-stage stochastic linear semi-infinite programming with recourse to handle uncertainty in data defining (deterministic) linear semi-infinite programming. We develop and analyze volumetric barrier decomposition-based interior point methods for solving this class of optimization problems, and present a complexity analysis of the proposed algorithms. We establish our convergence analysis by … Read more