Second-Order Strong Optimality and Second-Order Duality for Nonsmooth Constrained Multiobjective Fractional Programming Problems

  • Chen Jiawei
  • Luyu Liu
  • Jen-Chih Yao
    • Categories Multi-Criteria Optimization, Nonsmooth Optimization Tags , , , ,

    \(\) This paper investigates constrained nonsmooth multiobjective fractional programming problem (NMFP) in real Banach spaces. It derives a quotient calculus rule for computing the first- and second-order Clarke derivatives of fractional functions involving locally Lipschitz functions. A novel second-order Abadie-type regularity condition is presented, defined with the help of the Clarke directional derivative and the … Read more

    The Balanced Facility Location Problem: Complexity and Heuristics

  • Malena Schmidt
  • Bismark Singh
    • Categories Applications - OR and Management Sciences, Combinatorial Optimization Tags , , , ,

    In a recent work, Schmitt and Singh propose a new quadratic facility location model to address ecological challenges faced by policymakers in Bavaria, Germany. Building on this previous work, we significantly extend our understanding of this new problem. We develop connections to traditional combinatorial optimization models and show the problem is NP-hard. We then develop … Read more

    Slow convergence of the moment-SOS hierarchy for an elementary polynomial optimization problem

  • Didier Henrion
  • Adrien Le Franc
  • Victor Magron
    • Categories Convex Optimization, Nonlinear Optimization Tags , ,

    We describe a parametric univariate quadratic optimization problem for which the moment-SOS hierarchy has finite but increasingly slow convergence when the parameter tends to its limit value. We estimate the order of finite convergence as a function of the parameter. Article Download View Slow convergence of the moment-SOS hierarchy for an elementary polynomial optimization problem

    Adjustable Robust Nonlinear Network Design under Demand Uncertainties

  • Johannes Thürauf
  • Julia Grübel
  • Martin Schmidt
    • Categories (Mixed) Integer Nonlinear Programming, Energy, Robust Optimization Tags , , , ,

    We study network design problems for nonlinear and nonconvex flow models under demand uncertainties. To this end, we apply the concept of adjustable robust optimization to compute a network design that admits a feasible transport for all, possibly infinitely many, demand scenarios within a given uncertainty set. For solving the corresponding adjustable robust mixed-integer nonlinear … Read more

    On the integrality Gap of Small Asymmetric Travelling Salesman Problems: A Polyhedral and Computational Approach

  • Eleonora Vercesi
  • Luca Maria Gambardella
  • Stefano Gualandi
  • Monaldo Mastrolilli
  • Janos
    • Categories Combinatorial Optimization, Integer Programming, Linear, Cone and Semidefinite Programming Tags ,

    \(\) In this paper, we investigate the integrality gap of the Asymmetric Traveling Salesman Problem (ATSP) with respect to the linear relaxation given by the Asymmetric Subtour Elimination Problem (ASEP) for small-sized instances. In particular, we focus on the geometric properties and symmetries of the ASEP polytope ( \(P_{ASEP}^n\) ) and its vertices. The polytope’s … Read more

    Representing Integer Program Value Function with Neural Networks

  • Tu Anh-Nguyen
  • Joey Huchette
  • Andrew J. Schaefer
    • Categories (Mixed) Integer Linear Programming, Integer Programming Tags , ,

    We study the value function of an integer program (IP) by characterizing how its optimal value changes as the right-hand side varies. We show that the IP value function can be approximated to any desired degree of accuracy using machine learning (ML) techniques. Since an IP value function is a Chvátal-Gomory (CG) function, we first … Read more

    Frequency regulation with storage: On losses and profits

  • Dirk Lauinger
  • François Vuille
  • Daniel Kuhn
    • Categories Energy, Robust Optimization, Semi-infinite Programming Tags , , , , , ,

    Low-carbon societies will need to store vast amounts of electricity to balance intermittent generation from wind and solar energy, for example, through frequency regulation. Here, we derive an analytical solution to the decision-making problem of storage operators who sell frequency regulation power to grid operators and trade electricity on day-ahead markets. Mathematically, we treat future … Read more

    An inexact infeasible arc-search interior-point method for linear programming problems

  • Einosuke Iida
  • Makoto Yamashita
    • Categories Linear Programming, Linear, Cone and Semidefinite Programming

    Inexact interior-point methods (IPMs) are a type of interior-point methods that inexactly solve the linear equation system for obtaining the search direction. On the other hand, arc-search IPMs approximate the central path with an ellipsoidal arc obtained by solving two linear equation systems in each iteration, while conventional line-search IPMs solve one linear system, therefore, … Read more

    Stochastic Aspects of Dynamical Low-Rank Approximation in the Context of Machine Learning

  • Arsen Hnatiuk
  • Lisa Kusch
  • Jonas Kusch
  • Nicolas R. Gauger
  • Andrea Walther
    • Categories Data Science Theory, Nonlinear Optimization, Optimization in Data Science Tags , , , ,

    The central challenges of today’s neural network architectures are the prohibitive memory footprint and the training costs associated with determining optimal weights and biases. A large portion of research in machine learning is therefore dedicated to constructing memory-efficient training methods. One promising approach is dynamical low-rank training (DLRT) which represents and trains parameters as a … Read more

    Fast convergence of the primal-dual dynamical system and algorithms for a nonsmooth bilinearly coupled saddle point problem

  • Kewei Ding
  • Jörg Fliege
  • Phan Vuong
    • Categories Game Theory, Nonsmooth Optimization Tags , , , ,

    \(\) This paper is devoted to study the convergence rates of a second-order dynamical system and its corresponding discretizations associated with a nonsmooth bilinearly coupled convex-concave saddle point problem. We derive the convergence rate of the primal-dual gap for the second-order dynamical system with asymptotically vanishing damping term. Based on the implicit discretization, we propose … Read more