pareto optimality

Inexact scalarization proximal methods for multiobjective quasiconvex minimization on Hadamard manifold

  • Nancy Baygorrea
  • Nelson Maculan
  • Erik Alex Papa Quiroz
    • Categories Convex and Nonsmooth Optimization, Multi-Criteria Optimization, Nonsmooth Optimization Tags , , , ,

    In this paper we extend naturally the scalarization proximal point method to solve multiobjective unconstrained minimization problems, proposed by Apolinario et al.(2016), from Euclidean spaces to Hadamard manifolds for locally Lipschitz and quasiconvex vector objective functions. Moreover, we present a convergence analysis, under some mild assumptions on the multiobjective function, for two inexact variants of … Read more

    An external penalty-type method for multicriteria

  • Ellen H. Fukuda
  • L. M. Graña Drummond
  • Fernanda M. P. Raupp
    • Categories Constrained Nonlinear Optimization, Multi-Criteria Optimization Tags , , ,

    We propose an extension of the classical real-valued external penalty method to the multicriteria optimization setting. As its single objective counterpart, it also requires an external penalty function for the constraint set, as well as an exogenous divergent sequence of nonnegative real numbers, the so-called penalty parameters, but, differently from the scalar procedure, the vector-valued … Read more

    Minimum cost subset selection with two competing agents

  • Gaia Nicosia
  • Ulrich Pferschy
  • Andrea Pacifici
    • Categories Combinatorial Optimization, Game Theory Tags , , , , ,

    We address an optimization problem in which two agents, each with a set of weighted items, compete in order to minimize the total weight of their solution sets. The latter are built according to a sequential game consisting in a fixed number of rounds. In every round each agent submits one item that may be … Read more

    Robust and Stochastically Weighted Multi-Objective Optimization Models and Reformulations

  • Jian Hu
  • Sanjay Mehrotra
    • Categories Multi-Criteria Optimization, Robust Optimization, Stochastic Programming Tags , , ,

    In this paper we introduce robust and stochastically weighted sum approaches to deterministic and stochastic multi-objective optimization. The robust weighted sum approach minimizes the worst case weighted sum of objectives over a given weight region. We study the reformulations of the robust weighted sum problem under different definitions of deterministic weight regions. We next introduce … Read more

    Multi-group Support Vector Machines with measurement costs: a biobjective approach

  • Emilio Carrizosa
  • Belén Martín-Barragán
  • Dolores Romero Morales
    • Categories Data-Mining Tags , , ,

    Support Vector Machine has shown to have good performance in many practical classification settings. In this paper we propose, for multi-group classification, a biobjective optimization model in which we consider not only the generalization ability (modelled through the margin maximization), but also costs associated with the features. This cost is not limited to an economical … Read more