Francisco N. C. Sobral

Polynomial worst-case iteration complexity of quasi-Newton primal-dual interior point algorithms for linear programming

  • Francisco N. C. Sobral
  • Jacek Gondzio
    • Categories Linear Programming, Linear, Cone and Semidefinite Programming, Nonlinear Optimization Tags , , ,

    Quasi-Newton methods are well known techniques for large-scale numerical optimization. They use an approximation of the Hessian in optimization problems or the Jacobian in system of nonlinear equations. In the Interior Point context, quasi-Newton algorithms compute low-rank updates of the matrix associated with the Newton systems, instead of computing it from scratch at every iteration. … Read more

    On complexity constants of linear and quadratic models for derivative-free trust-region algorithms

  • A. E. Schwertner
  • Francisco N. C. Sobral
    • Categories Nonlinear Optimization Tags , , ,

    Complexity analysis has become an important tool in the convergence analysis of optimization algorithms. For derivative-free optimization algorithms, it is not different. Interestingly, several constants that appear when developing complexity results hide the dimensions of the problem. This work organizes several results in literature about bounds that appear in derivative-free trust-region algorithms based on linear … Read more

    A support tool for planning classrooms considering social distancing between students

  • J. C. Bortolete
  • Luís Felipe Bueno
  • R. Butkeraites
  • Antonio Chaves
  • G. Collaço
  • M. Magueta
  • Luiz Leduíno Salles Neto
  • T. Silva
  • Thiago P. Siqueira
  • Francisco N. C. Sobral
  • F. J. R. Pelogia
  • Horacio Hideki Yanasse
    • Categories Applications - OR and Management Sciences, Global Optimization, Optimization Software and Modeling Systems Tags , , , , ,

    In this paper, we present the online tool salaplanejada.unifesp.br developed to assist the layout planning of classrooms considering the social distance in the context of the COVID-19 pandemic. We address both the allocation problem in rooms where seats are fixed as well as the problem in rooms where seats can be moved freely. For the … Read more

    A robust method based on LOVO functions for solving least squares problems

  • E. V. Castelani
  • R. Lopes
  • W. V. I. Shirabayashi
  • Francisco N. C. Sobral
    • Categories Nonlinear Systems and Least-Squares, Nonsmooth Optimization, Parallel Algorithms Tags , , ,

    The robust adjustment of nonlinear models to data is considered in this paper. When data comes from real experiments, it is possible that measurement errors cause the appearance of discrepant values, which should be ignored when adjusting models to them. This work presents a Lower Order-value Optimization (LOVO) version of the Levenberg-Marquardt algorithm, which is … Read more

    Quasi-Newton approaches to Interior Point Methods for quadratic problems

  • Jacek Gondzio
  • Francisco N. C. Sobral
    • Categories Nonlinear Systems and Least-Squares, Quadratic Programming Tags , , , ,

    Interior Point Methods (IPM) rely on the Newton method for solving systems of nonlinear equations. Solving the linear systems which arise from this approach is the most computationally expensive task of an interior point iteration. If, due to problem’s inner structure, there are special techniques for efficiently solving linear systems, IPMs enjoy fast convergence and … Read more

    Global convergence of a derivative-free inexact restoration filter algorithm for nonlinear programming

  • Priscila Savulski Ferreira
  • Elizabeth Wegner Karas
  • Mael Sachine
  • Francisco N. C. Sobral
    • Categories Constrained Nonlinear Optimization Tags , , , , ,

    In this work we present an algorithm for solving constrained optimization problems that does not make explicit use of the objective function derivatives. The algorithm mixes an inexact restoration framework with filter techniques, where the forbidden regions can be given by the flat or slanting filter rule. Each iteration is decomposed in two independent phases: … Read more

    Inexact Restoration method for Derivative-Free Optimization with smooth constraints

  • Luís Felipe Bueno
  • A. Friedlander
  • José Mario Martínez
  • Francisco N. C. Sobral
    • Categories Constrained Nonlinear Optimization, Nonlinear Optimization, Optimization Software and Modeling Systems Tags , , ,

    A new method is introduced for solving constrained optimization problems in which the derivatives of the constraints are available but the derivatives of the objective function are not. The method is based on the Inexact Restoration framework, by means of which each iteration is divided in two phases. In the first phase one considers only … Read more

    Constrained Derivative-Free Optimization on Thin Domains

  • José Mario Martínez
  • Francisco N. C. Sobral
    • Categories Constrained Nonlinear Optimization, Global Optimization Applications, Nonlinear Optimization Tags , , , ,

    Many derivative-free methods for constrained problems are not efficient for minimizing functions on “thin” domains. Other algorithms, like those based on Augmented Lagrangians, deal with thin constraints using penalty-like strategies. When the constraints are computationally inexpensive but highly nonlinear, these methods spend many potentially expensive objective function evaluations motivated by the difficulties of improving feasibility. … Read more