Multi-Criteria Optimization

Generalized polarity and weakest constraint qualifications in multiobjective optimization

  • Oliver Stein
  • Maximilian Volk
    • Categories Multi-Criteria Optimization Tags , , , ,

    In G. Haeser, A. Ramos, Constraint Qualifications for Karush-Kuhn-Tucker Conditions in Multiobjective Optimization, JOTA, Vol.~187 (2020), 469-487, a generalization of the normal cone from single objective to multiobjective optimization is introduced, along with a weakest constraint qualification such that any local weak Pareto optimal point is a weak Kuhn-Tucker point. We extend this approach to … Read more

    Relaxations and Duality for Multiobjective Integer Programming

  • Alex Dunbar
  • Saumya Sinha
  • Andrew J. Schaefer
    • Categories Integer Programming, Multi-Criteria Optimization Tags , , , ,

    Multiobjective integer programs (MOIPs) simultaneously optimize multiple objective func- tions over a set of linear constraints and integer variables. In this paper, we present continuous, convex hull and Lagrangian relaxations for MOIPs and examine the relationship among them. The convex hull relaxation is tight at supported solutions, i.e., those that can be derived via a … Read more

    Computing Tchebychev weight space decomposition for multiobjective discrete optimization problems

  • Tyler Perini
    • Categories Integer Programming, Multi-Criteria Optimization, Optimization in Data Science Tags , , ,

    Multiobjective discrete optimization (MODO) techniques, including weight space decomposition, have received increasing attention in the last decade. The primary weight space decomposition technique in the literature is defined for the weighted sum utility function, through which sets of weights are assigned to a subset of the nondominated set. Recent work has begun to study the … Read more

    Computing an enclosure for multiobjective mixed-integer nonconvex optimization problems using piecewise linear relaxations

  • Moritz Link
  • Stefan Volkwein
    • Categories (Mixed) Integer Nonlinear Programming, Multi-Criteria Optimization, Network Optimization Tags , , , ,

    In this paper, a new method for computing an enclosure of the nondominated set of multiobjective mixed-integer problems without any convexity requirements is presented. In fact, our criterion space method makes use of piecewise linear relaxations in order to bypass the nonconvexity of the original problem. The method chooses adaptively which level of relaxation is … Read more

    A unified scheme for scalarization in set optimization

  • Xuan Duc Ha Truong
    • Categories Multi-Criteria Optimization Tags , , ,

    In this work, we propose a new scheme for scalarization in set optimization studied with the Kuroiwa set appoach. First, we define an abstract scalarizing function possessing properties such as global Lipschizity, sublinearity, cone monotonicity, cone representation property, cone interior representation property and uniform positivity. Next, we use this function to define the so called … Read more

    A Reduced Jacobian Scheme with Full Convergence for Multicriteria Optimization

  • Mounir El Maghri
  • Youssef Elboulqe
    • Categories Constrained Nonlinear Optimization, Linear Programming, Multi-Criteria Optimization Tags , , , , ,

    In this paper, we propose a variant of the reduced Jacobian method (RJM) introduced by El Maghri and Elboulqe in [JOTA, 179 (2018) 917–943] for multicriteria optimization under linear constraints. Motivation is that, contrarily to RJM which has only global convergence to Pareto KKT-stationary points in the classical sense of accumulation points, this new variant … Read more

    A Proximal Gradient Method for Multi-objective Optimization Problems Using Bregman Functions

  • Md Abu Talhamainuddin Ansary
  • Joydeep Dutta
    • Categories Convex Optimization, Multi-Criteria Optimization, Nonsmooth Optimization Tags , , , ,

    In this paper, a globally convergent proximal gradient method is developed for convex multi-objective optimization problems using Bregman distance. The proposed method is free from any kind of a priori chosen parameters or ordering information of objective functions. At every iteration of the proposed method, a subproblem is solved to find a descent direction. This … Read more

    Integral Global Optimality Conditions and an Algorithm for Multiobjective Problems

  • Everton Silva
  • Elizabeth Wegner Karas
  • Lucelina Santos
    • Categories Multi-Criteria Optimization, Nonlinear Optimization, Nonsmooth Optimization Tags , , , ,

    In this work, we propose integral global optimality conditions for multiobjective problems not necessarily differentiable. The integral characterization, already known for single objective problems, are extended to multiobjective problems by weighted sum and Chebyshev weighted scalarizations. Using this last scalarization, we propose an algorithm for obtaining an approximation of the weak Pareto front whose effectiveness … Read more

    Duality assertions in vector optimization w.r.t. relatively solid convex cones in real linear spaces

  • Christian Günther
  • Bahareh Khazayel
  • Christiane Tammer
    • Categories Constrained Nonlinear Optimization, Multi-Criteria Optimization Tags , , , , , , ,

    We derive duality assertions for vector optimization problems in real linear spaces based on a scalarization using recent results concerning the concept of relative solidness for convex cones (i.e., convex cones with nonempty intrinsic cores). In our paper, we consider an abstract vector optimization problem with generalized inequality constraints and investigate Lagrangian type duality assertions … Read more

    Advancements in the computation of enclosures for multi-objective optimization problems

  • Gabriele Eichfelder
  • Leo Warnow
    • Categories (Mixed) Integer Nonlinear Programming, Multi-Criteria Optimization, Nonlinear Optimization Tags , , , ,

    A central goal for multi-objective optimization problems is to compute their nondominated sets. In most cases these sets consist of infinitely many points and it is not a practical approach to compute them exactly. One solution to overcome this problem is to compute an enclosure, a special kind of coverage, of the nondominated set. One … Read more