Distributionally Robust Optimization under Decision-Dependent Ambiguity Set with an Application to Machine Scheduling

  • Miguel A. Lejeune
  • Nilay Noyan
  • Gabor Rudolf
    • Categories Scheduling, Stochastic Programming

    We introduce a new class of distributionally robust optimization problems under decision dependent ambiguity sets. In particular, as our ambiguity sets, we consider balls centered on a decision-dependent probability distribution. The balls are based on a class of earth mover’s distances that includes both the total variation distance and the Wasserstein metrics. We discuss the … Read more

    A Mixed-Integer PDE-Constrained Optimization Formulation for Electromagnetic Cloaking

  • Sven Leyffer
  • Todd S. Munson
  • Ryan Vogt
    • Categories (Mixed) Integer Nonlinear Programming, Applications - Science and Engineering, Optimization of Systems modeled by PDEs Tags , , ,

    We formulate a mixed-integer partial-differential equation constrained optimization problem for designing an electromagnetic cloak governed by the 2D Helmholtz equation with absorbing boundary conditions. Our formulation is an alternative to the topology optimization formulation of electromagnetic cloaking design. We extend the formulation to include uncertainty with respect to the angle of the incidence wave, and … Read more

    A primal-dual modified log-barrier method for inequality constrained nonlinear optimization

  • Joshua D. Griffin
  • Riadh Omheni
    • Categories Constrained Nonlinear Optimization, Nonlinear Optimization Tags , , , ,

    We present a primal-dual modified log-barrier algorithm to solve inequality constrained nonlinear optimization problems. Basically, the algorithm is a Newton-like method applied to a perturbation of the optimality system that follows from a reformulation of the initial problem by introducing a modified log-barrier function to handle inequality constraints. The algorithm uses an outer/inner iteration scheme … Read more

    Weakly Homogeneous Optimization Problems

  • Vu Trung Hieu
    • Categories Nonlinear Optimization Tags , , , , , ,

    This paper investigates a new class of optimization problems whose objective functions are weakly homogeneous relative to the constrain sets. Two sufficient conditions for nonemptiness and boundedness of solution sets are established. We also study linear parametric problems and upper semincontinuity of the solution map. ArticleDownload View PDF

    Dimension in Polynomial Variational Inequalities

  • Vu Trung Hieu
    • Categories Complementarity and Variational Inequalities Tags , , , ,

    The aim of the paper is twofold. Firstly, by using the constant rank level set theorem from differential geometry, we establish sharp upper bounds for the dimensions of the solution sets of polynomial variational inequalities under mild conditions. Secondly, a classification of polynomial variational inequalities based on dimensions of their solution sets is introduced and … Read more

    Equilibrium selection for multi-portfolio optimization

  • Lorenzo Lampariello
  • Christoph Neumann
  • Simone Sagratella
  • Oliver Stein
  • Jacopo Maria Ricci
    • Categories Complementarity and Variational Inequalities, Finance and Economics Tags , , , ,

    This paper studies a Nash game arising in portfolio optimization. We introduce a new general multi-portfolio model and state sufficient conditions for the monotonicity of the underlying Nash game. This property allows us to treat the problem numerically and, for the case of nonunique equilibria, to solve hierarchical problems of equilibrium selection. We also give … Read more

    On Modeling Local Search with Special-Purpose Combinatorial Optimization Hardware

  • Xiaoyuan Liu
  • Avradip Mandal
  • Arnab Roy
  • Ilya Safro
  • Sarvagya Upadhyay
  • Hayato Ushijima-Mwesigwa
    • Categories Combinatorial Optimization, Meta Heuristics Tags , , ,

    As we approach the physical limits predicted by Moore’s law, a variety of specialized hardware is emerging to tackle specialized tasks in different domains. Within combinatorial optimization, adiabatic quantum computers, CMOS annealers, and optical parametric oscillators are few of the emerging specialized hardware technology aimed at solving optimization problems. In terms of mathematical framework, the … Read more

    The maximum hBccolorable subgraph problem and related problems

  • Olga Kuryatnikova
  • Renata Sotirov
  • Juan C. Vera
    • Categories Semi-definite Programming

    The maximum $k$-colorable subgraph (M$k$CS) problem is to find an induced $k$-colorable subgraph with maximum cardinality in a given graph. This paper is an in-depth analysis of the M$k$CS problem that considers various semidefinite programming relaxations including their theoretical and numerical comparisons. To simplify these relaxations we exploit the symmetry arising from permuting the colors, … Read more

    Gamma-Robust Electricity Market Equilibrium Models with Transmission and Generation Investments

  • Emre Çelebi
  • Vanessa Krebs
  • Martin Schmidt
    • Categories Applications - OR and Management Sciences, Robust Optimization Tags , , , ,

    We consider uncertain robust electricity market equilibrium problems including transmission and generation investments. Electricity market equilibrium modeling has a long tradition but is, in most of the cases, applied in a deterministic setting in which all data of the model are known. Whereas there exist some literature on stochastic equilibrium problems, the field of robust … Read more

    Imposing contiguity constraints in political districting models

  • Austin Buchanan
  • Eugene Lykhovyd
  • Hamidreza Validi
    • Categories Applications - OR and Management Sciences, Combinatorial Optimization, Integer Programming

    Beginning in the 1960s, techniques from operations research began to be used to generate political districting plans. A classical example is the integer programming model of Hess et al. (Operations Research 13(6):998–1006, 1965). Due to the model’s compactness-seeking objective, it tends to generate contiguous or nearly-contiguous districts, although none of the model’s constraints explicitly impose … Read more