Multi-Criteria Optimization

Cut Generation for Optimization Problems with Multivariate Risk Constraints

  • Simge Küçükyavuz
  • Nilay Noyan
    • Categories Integer Programming, Multi-Criteria Optimization, Stochastic Programming

    We consider a class of multicriteria stochastic optimization problems that features benchmarking constraints based on conditional value-at-risk and second-order stochastic dominance. We develop alternative mixed-integer programming formulations and solution methods for cut generation problems arising in optimization under such multivariate risk constraints. We give the complete linear description of two non-convex substructures appearing in these … Read more

    Branch-and-bound for bi-objective integer programming

  • Sophie N. Parragh
  • Fabien Tricoire
    • Categories Combinatorial Optimization, Integer Programming, Multi-Criteria Optimization Tags , , , ,

    In Pareto bi-objective integer optimization the optimal result corresponds to a set of non- dominated solutions. We propose a generic bi-objective branch-and-bound algorithm that uses a problem-independent branching rule exploiting available integer solutions, and cutting plane generation taking advantage of integer objective values. The developed algorithm is applied to the bi-objective team orienteering problem with … Read more

    On Global Optimization

  • Isaac Siwale
    • Categories (Mixed) Integer Nonlinear Programming, Global Optimization, Multi-Criteria Optimization Tags , , , ,

    This paper presents a relatively “unfettered” method for finding global optima to constrained nonlinear programs. The method reformulates the given program into a bi-objective mixed-integer program that is then solved for the Nash equilibrium. A numerical example (whose solution provides a new benchmark against which other algorithms may be assessed) is included to illustrate the … Read more

    A dynamic gradient approach to Pareto optimization with nonsmooth nonconvex objective functions

  • Hédy Attouch
  • Guillaume Garrigos
  • Xavier Goudou
    • Categories Convex and Nonsmooth Optimization, Multi-Criteria Optimization

    In a general Hilbert framework, we consider continuous gradient-like dynamical systems for constrained multiobjective optimization involving non-smooth convex objective functions. Our approach is in the line of a previous work where was considered the case of convex di erentiable objective functions. Based on the Yosida regularization of the subdi erential operators involved in the system, we obtain … Read more

    On the effects of combining objectives in multi-objective optimization

  • Stephan Dempe
  • Gabriele Eichfelder
  • Jörg Fliege
    • Categories Multi-Criteria Optimization

    In multi-objective optimization, one considers optimization problems with more than one objective function, and in general these objectives conflict each other. As the solution set of a multiobjective problem is often rather large and contains points of no interest to the decision-maker, strategies are sought that reduce the size of the solution set. One such … Read more

    Minimal Points, Variational Principles, and Variable Preferences in Set Optimization

  • Boris S. Mordukhovich
  • Antoine Soubeyran
  • Bao Q. Truong
    • Categories Convex and Nonsmooth Optimization, Multi-Criteria Optimization, Nonlinear Optimization

    The paper is devoted to variational analysis of set-valued mappings acting from quasimetric spaces into topological spaces with variable ordering structures. Besides the mathematical novelty, our motivation comes from applications to adaptive dynamical models of behavioral sciences. We develop a unified dynamical approach to variational principles in such settings based on the new minimal point … Read more

    Approximating Pareto Curves using Semidefinite Relaxations

  • Didier Henrion
  • Jean-Bernard Lasserre
  • Victor Magron
    • Categories Multi-Criteria Optimization, Semi-definite Programming

    We consider the problem of constructing an approximation of the Pareto curve associated with the multiobjective optimization problem $\min_{x \in S} \{(f_1(x),f_2(x))\}$, where $f_1$ and $f_2$ are two conflicting positive polynomial criteria and $S \subset R^n$ is a compact basic semialgebraic set. We provide a systematic numerical scheme to approximate the Pareto curve. We start … Read more

    Surrogate upper bound sets for bi-objective bi-dimensional binary knapsack problems

  • Audrey Cerqueus
  • Xavier Gandibleux
  • Anthony Przybylski
    • Categories Combinatorial Optimization, Multi-Criteria Optimization Tags , , , ,

    The paper deals with the definition and the computation of surrogate upper bound sets for the bi-objective bi-dimensional binary knapsack problem. It introduces the Optimal Convex Surrogate Upper Bound set, which is the tightest possible definition based on the convex relaxation of the surrogate relaxation. Two exact algorithms are proposed: an enumerative algorithm and its … Read more

    Fixed points and variational principles with applications to capability theory of wellbeing via variational rationality

  • Boris S. Mordukhovich
  • Antoine Soubeyran
  • Bao Q. Truong
    • Categories Applications - OR and Management Sciences, Multi-Criteria Optimization, Nonsmooth Optimization Tags , , , ,

    In this paper we first develop two new results of variational analysis. One is a fixed point theorem for parametric dynamic systems in quasimetric spaces, which can also be interpreted as an existence theorem of minimal points with respect to reflexive and transitive preferences for sets in products spaces. The other one is a variational … Read more

    A Scalarization Proximal Point Method for Quasiconvex Multiobjective Minimization

  • H. C. F. Apolinário
  • Paulo Roberto Oliveira
  • Erik Alex Papa Quiroz
    • Categories Generalized Convexity/Monoticity, Multi-Criteria Optimization, Nonsmooth Optimization Tags , , , , ,

    In this paper we propose a scalarization proximal point method to solve multiobjective unconstrained minimization problems with locally Lipschitz and quasiconvex vector functions. We prove, under natural assumptions, that the sequence generated by the method is well defined and converges globally to a Pareto-Clarke critical point. Our method may be seen as an extension, for … Read more