Worst-case evaluation complexity of regularization methods for smooth unconstrained optimization using Hölder continuous gradients

  • Coralia Cartis
  • Nicholas I. M. Gould
  • Philippe L. Toint
    • Categories Unconstrained Optimization Tags , ,

    The worst-case behaviour of a general class of regularization algorithms is considered in the case where only objective function values and associated gradient vectors are evaluated. Upper bounds are derived on the number of such evaluations that are needed for the algorithm to produce an approximate first-order critical point whose accuracy is within a user-defined … Read more

    Modeling Two-Dimensional Guillotine Cutting Problems via Integer Programming

  • Fabio Furini
  • Enrico Malaguti
  • Dimitri Thomopulos
    • Categories Integer Programming

    We propose a framework to model general guillotine restrictions in two-dimensional cutting problems formulated as Mixed Integer Linear Programs (MIP). The modeling framework requires a pseudo-polynomial number of variables and constraints, which can be effectively enumerated for medium-size instances. Our modeling of general guillotine cuts is the first one that, once it is implemented within … Read more

    The Value of Flexibility in Robust Location-Transportation Problems

  • Amir Ardestani-Jaafari
  • Erick Delage
    • Categories Facility Planning and Design, Robust Optimization, Transportation Tags , , , , ,

    This article studies a multi-period capacitated fixed-charge location-transportation problem in which, while the location and capacity of each facility need to be determined immediately, the determination of final production and distribution of products can be delayed until actual orders are received in each period. In contexts where little is known about future demand, robust optimization, … Read more

    On the Coherent Risk Measure Representations in the Discrete Probability Spaces

  • Kerem Ugurlu
    • Categories Applications - OR and Management Sciences

    We give a complete characterization of both comonotone and not comonotone coherent risk measures in the discrete finite probability space, where each outcome is equally likely. To the best of our knowledge, this is the first work that characterizes and distinguishes comonotone and not comonotone coherent risk measures via a simplified AVaR representation in this … Read more

    Convergence analysis for Lasserre’s measure–based hierarchy of upper bounds for polynomial optimization

  • Etienne de Klerk
  • Monique Laurent
  • Zhao Sun
    • Categories Global Optimization Theory, Semi-definite Programming Tags

    We consider the problem of minimizing a continuous function f over a compact set K. We analyze a hierarchy of upper bounds proposed by Lasserre in [SIAM J. Optim. 21(3) (2011), pp. 864-􀀀885], obtained by searching for an optimal probability density function h on K which is a sum of squares of polynomials, so that … Read more

    Solving Power-Constrained Gas Transportation Problems using an MIP-based Alternating Direction Method

  • Björn Geißler
  • Antonio Morsi
  • Lars Schewe
  • Martin Schmidt
    • Categories (Mixed) Integer Nonlinear Programming, Applications - Science and Engineering, Constrained Nonlinear Optimization Tags , , , ,

    We present a solution algorithm for problems from steady-state gas transport optimization. Due to nonlinear and nonconvex physics and engineering models as well as discrete controllability of active network devices, these problems lead to hard nonconvex mixed-integer nonlinear optimization models. The proposed method is based on mixed-integer linear techniques using piecewise linear relaxations of the … Read more

    Error Bounds and Holder Metric Subregularity

  • Alexander Y. Kruger
    • Categories Convex and Nonsmooth Optimization

    The Holder setting of the metric subregularity property of set-valued mappings between general metric or Banach/Asplund spaces is investigated in the framework of the theory of error bounds for extended real-valued functions of two variables. A classification scheme for the general Holder metric subregularity criteria is presented. The criteria are formulated in terms of several … Read more

    Sample approximations of multiobjective stochastic optimization problems

  • Bogdan V. Norkin
    • Categories Finance and Economics, Multi-Criteria Optimization, Stochastic Programming Tags , , , , ,

    The article describes approximation technique for solving multiobjective stochastic optimization problems. As a generalized model of a stochastic system to be optimized a vector “input — random output” system is used. Random outputs are converted into a vector of deterministic performance/risk indicators. The problem is to find those inputs that correspond to Pareto-optimal values of … Read more

    Multistage Robust Mixed Integer Optimization with Adaptive Partitions

  • Dimitris Bertsimas
  • Iain Dunning
    • Categories Robust Optimization Tags ,

    We present a new partition-and-bound method for multistage adaptive mixed integer optimization (AMIO) problems that extends previous work on finite adaptability. The approach analyzes the optimal solution to a static (non-adaptive) version of an AMIO problem to gain insight into which regions of the uncertainty set are restricting the objective function value. We use this … Read more

    Semivectorial Bilevel Optimization on Riemannian Manifolds

  • Henri Bonnel
  • Leonard Todjihounde
  • Constantin Udriste
    • Categories Nonlinear Optimization Tags , ,

    In this paper we deal with the semivectorial bilevel problem in the Riemannian setting. The upper level is a scalar optimization problem to be solved by the leader, and the lower level is a multiobjective optimization problem to be solved by several followers acting in a cooperative way inside the greatest coalition and choosing among … Read more