Ana Luisa Custódio

Nonlinear Derivative-free Constrained Optimization with a Mixed Penalty-Logarithmic Barrier Approach and Direct Search

  • Andrea Brilli
  • Ana Luisa Custódio
  • Giampaolo Liuzzi
  • Everton Silva
    • Categories Constrained Nonlinear Optimization Tags , , ,

    In this work, we propose the joint use of a mixed penalty-logarithmic barrier approach and generating set search, for addressing nonlinearly constrained derivative-free optimization problems. A merit function is considered, wherein the set of inequality constraints is divided into two groups: one treated with a logarithmic barrier approach, and another, along with the equality constraints, … 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

    Derivative-free separable quadratic modeling and cubic regularization for unconstrained optimization

  • Ana Luisa Custódio
  • R. Garmanjani
  • Marcos Raydan
    • Categories Unconstrained Optimization Tags , , , ,

    We present a derivative-free separable quadratic modeling and cubic regularization technique for solving smooth unconstrained minimization problems. The derivative-free approach is mainly concerned with building a quadratic model that could be generated by numerical interpolation or using a minimum Frobenious norm approach, when the number of points available does not allow to build a complete … Read more

    Parallel Strategies for Direct Multisearch

  • C. P. Brás
  • Ana Luisa Custódio
  • S. Tavares
  • V. Duarte
  • P. Medeiros
    • Categories Bound-constrained Optimization, Multi-Criteria Optimization, Parallel Algorithms

    Direct Multisearch (DMS) is a Derivative-free Optimization class of algorithms suited for computing approximations to the complete Pareto front of a given Multiobjective Optimization problem. It has a well-supported convergence analysis and simple implementations present a good numerical performance, both in academic test sets and in real applications. Recently, this numerical performance was improved with … Read more

    Using first-order information in Direct Multisearch for multiobjective optimization

  • Roberto Andreani
  • Ana Luisa Custódio
  • Marcos Raydan
    • Categories Bound-constrained Optimization, Multi-Criteria Optimization, Nonlinear Optimization Tags , , , ,

    Derivatives are an important tool for single-objective optimization. In fact, it is commonly accepted that derivative-based methods present a better performance than derivative-free optimization approaches. In this work, we will show that the same does not apply to multiobjective derivative-based optimization, when the goal is to compute an approximation to the complete Pareto front of … Read more

    Worst-case Complexity Bounds of Directional Direct-search Methods for Multiobjective Optimization

  • Ana Luisa Custódio
  • Youssef Diouane
  • R. Garmanjani
  • Elisa Riccietti
    • Categories Nonlinear Optimization, Unconstrained Optimization

    Direct Multisearch is a well-established class of algorithms, suited for multiobjective derivative-free optimization. In this work, we analyze the worst-case complexity of this class of methods in its most general formulation for unconstrained optimization. Considering nonconvex smooth functions, we show that to drive a given criticality measure below a specific positive threshold, Direct Multisearch takes … Read more

    On the use of polynomial models in multiobjective directional direct search

  • C. P. Brás
  • Ana Luisa Custódio
    • Categories Nonlinear Optimization Tags , , , ,

    Polynomial interpolation or regression models are an important tool in Derivative-free Optimization, acting as surrogates of the real function. In this work, we propose the use of these models in the multiobjective framework of directional direct search, namely the one of Direct Multisearch. Previously evaluated points are used to build quadratic polynomial models, which are … Read more

    A global hybrid derivative-free method for large-scale systems of nonlinear equations

  • Rodolfo Begiato
  • Ana Luisa Custódio
  • Márcia Aparecida Gomes-Ruggiero
    • Categories Nonlinear Optimization

    This work concerns the numerical solution of large-scale systems of nonlinear equations, when derivatives are not available for use, but assuming that all functions defining the problem are continuously differentiable. A hybrid approach is taken, based on a derivative-free iterative method, organized in three phases. The first phase is defined by derivative-free versions of a … Read more

    MultiGLODS: Global and Local Multiobjective Optimization using Direct Search

  • Ana Luisa Custódio
  • J. F. A. Madeira
    • Categories Global Optimization, Nonlinear Optimization Tags , , , ,

    The optimization of multimodal functions is a challenging task, in particular when derivatives are not available for use. Recently, in a directional direct search framework, a clever multistart strategy was proposed for global derivative-free optimization of single objective functions. The goal of the current work is to generalize this approach to the computation of global … Read more

    GLODS: Global and Local Optimization using Direct Search

  • Ana Luisa Custódio
  • J. F. A. Madeira
    • Categories Global Optimization Theory Tags , , , ,

    Locating and identifying points as global minimizers is, in general, a hard and time-consuming task. Difficulties increase when the derivatives of the functions defining the problem are not available for use. In this work, we propose a new class of methods suited for global derivative-free constrained optimization. Using direct search of directional type, the algorithm … Read more