multiobjective optimization

Scaled Proximal Gradient Methods for Multiobjective Optimization: Improved Linear Convergence and Nesterov’s Acceleration

  • Jian Chen
    • Categories Multi-Criteria Optimization Tags , , ,

    Over the past two decades, descent methods have received substantial attention within the multiobjective optimization field. Nonetheless, both theoretical analyses and empirical evidence reveal that existing first-order methods for multiobjective optimization converge slowly, even for well-conditioned problems, due to the objective imbalances. To address this limitation, we incorporate curvature information to scale each objective within … Read more

    On Subproblem Tradeoffs in Decomposition for Multiobjective Optimization

  • Philip de Castro
  • Margaret Wiecek
    • Categories Multi-Criteria Optimization Tags , ,

    Multiobjective optimization is widely used in applications for modeling and solving complex decision-making problems. To help resolve computational and cognitive difficulties associated with problems which have more than 3 or 4 objectives, we propose a decomposition and coordination methodology to support decision making for large multiobjective optimization problems (MOPs) with global, quasi-global, and local variables. … Read more

    On Necessary Optimality Conditions for Sets of Points in Multiobjective Optimization

  • Andrea Cristofari
  • Marianna De Santis
  • Stefano Lucidi
    • Categories Multi-Criteria Optimization Tags , ,

    Taking inspiration from what is commonly done in single-objective optimization, most local algorithms proposed for multiobjective optimization extend the classical iterative scalar methods and produce sequences of points able to converge to single efficient points. Recently, a growing number of local algorithms that build sequences of sets has been devised, following the real nature of … Read more

    A Subspace Minimization Barzilai-Borwein Method for Multiobjective Optimization Problems

  • Jian Chen
    • Categories Multi-Criteria Optimization Tags , , ,

    Nonlinear conjugate gradient methods have recently garnered significant attention within the multiobjective optimization community. These methods aim to maintain consistency in conjugate parameters with their single-objective optimization counterparts. However, the preservation of the attractive conjugate property of search directions remains uncertain, even for quadratic cases, in multiobjective conjugate gradient methods. This loss of interpretability of … Read more

    Preconditioned Barzilai-Borwein Methods for Multiobjective Optimization Problems

  • Jian Chen
    • Categories Multi-Criteria Optimization Tags , , ,

    Preconditioning is a powerful approach for solving ill-conditioned problems in optimization, where a preconditioning matrix is used to reduce the condition number and speed up the convergence of first-order method. Unfortunately, it is impossible to capture the curvature of all objective functions with a single preconditioning matrix in multiobjective optimization. Instead, second-order methods for multiobjective … Read more

    An Inexact Restoration Direct Multisearch Filter Approach to Multiobjective Constrained Derivative-free Optimization

  • Everton Silva
  • Ana Luisa Custódio
    • Categories Constrained Nonlinear Optimization, Nonsmooth Optimization Tags , , , , , ,

    Direct Multisearch (DMS) is a well-established class of methods for multiobjective derivative-free optimization, where constraints are addressed by an extreme barrier approach, only evaluating feasible points. In this work, we propose a filter approach, combined with an inexact feasibility restoration step, to address constraints in the DMS framework. The filter approach treats feasibility as an … Read more

    The convergence rate of the Sandwiching algorithm for convex bounded multiobjective optimization

  • Ina Lammel
  • Karl-Heinz Küfer
    • Categories Convex Optimization, Multi-Criteria Optimization Tags , , ,

    Sandwiching algorithms, also known as Benson-type algorithms, approximate the nondominated set of convex bounded multiobjective optimization problems by constructing and iteratively improving polyhedral inner and outer approximations. Using a set-valued metric, an estimate of the approximation quality is determined as the distance between the inner and outer approximation. The convergence of the algorithm is evaluated … Read more

    Global convergence of a BFGS-type algorithm for nonconvex multiobjective optimization problems

  • Leandro Fonseca Prudente
  • D. R. Souza
    • Categories Multi-Criteria Optimization Tags , , , , , ,

    We propose a modified BFGS algorithm for multiobjective optimization problems with global convergence, even in the absence of convexity assumptions on the objective functions. Furthermore, we establish the superlinear convergence of the method under usual conditions. Our approach employs Wolfe step sizes and ensures that the Hessian approximations are updated and corrected at each iteration … Read more

    Using dual relaxations in multiobjective mixed-integer quadratic programming

  • Marianna De Santis
  • Gabriele Eichfelder
  • Daniele Patria
  • Leo Warnow
    • Categories (Mixed) Integer Nonlinear Programming, Multi-Criteria Optimization Tags , , ,

    We present a branch-and-bound method for multiobjective mixed-integer convex quadratic programs that computes a superset of efficient integer assignments and a coverage of the nondominated set. The method relies on outer approximations of the upper image set of continuous relaxations. These outer approximations are obtained addressing the dual formulations of specific subproblems where the values … Read more

    Test Instances for Multiobjective Mixed-Integer Nonlinear Optimization

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

    A suitable set of test instances, also known as benchmark problems, is a key ingredient to systematically evaluate numerical solution algorithms for a given class of optimization problems. While in recent years several solution algorithms for the class of multiobjective mixed-integer nonlinear optimization problems have been proposed, there is a lack of a well-established set … Read more