Ladislav Lukšan

New class of limited-memory variationally-derived variable metric methods

  • Ladislav Lukšan
  • Jan Vlček
    • Categories Nonlinear Optimization Tags , ,

    A new family of limited-memory variationally-derived variable metric or quasi-Newton methods for unconstrained minimization is given. The methods have quadratic termination property and use updates, invariant under linear transformations. Some encouraging numerical experience is reported. Citation Technical Report V-973. Prague, ICS AS CR 2006. Article Download View New class of limited-memory variationally-derived variable metric methods

    Primal interior-point method for large sparse minimax optimization.

  • Ladislav Lukšan
  • Ctirad Matonoha
  • Jan Vlček
    • Categories Nonlinear Optimization, Nonsmooth Optimization Tags ,

    In this paper, we propose an interior-point method for large sparse minimax optimization. After a short introduction, where various barrier terms are discussed, the complete algorithm is introduced and some implementation details are given. We prove that this algorithm is globally convergent under standard mild assumptions. Thus nonconvex problems can be solved successfully. The results … Read more

    Trust-region interior-point method for large sparse l_1 optimization.

  • Ladislav Lukšan
  • Ctirad Matonoha
  • Jan Vlček
    • Categories Nonsmooth Optimization, Unconstrained Optimization Tags ,

    In this paper, we propose an interior-point method for large sparse l_1 optimization. After a short introduction, the complete algorithm is introduced and some implementation details are given. We prove that this algorithm is globally convergent under standard mild assumptions. Thus nonconvex problems can be solved successfully. The results of computational experiments given in this … Read more

    Variable metric method for minimization of partially separable nonsmooth functions.

  • Ladislav Lukšan
  • Jan Vlček
    • Categories Nonsmooth Optimization, Unconstrained Optimization Tags ,

    In this report, we propose a new partitioned variable metric method for minimization of nonsmooth partially separable functions. After a short introduction, the complete algorithm is introduced and some implementation details are given. We prove that this algorithm is globally convergent under standard mild assumptions. Computational experiments given confirm efficiency and robustness of the new … Read more

    A shifted Steihaug-Toint method for computing a trust-region step.

  • Ladislav Lukšan
  • Ctirad Matonoha
  • Jan Vlček
    • Categories Unconstrained Optimization Tags , , , , ,

    Trust-region methods are very convenient in connection with the Newton method for unconstrained optimization. The More-Sorensen direct method and the Steihaug-Toint iterative method are most commonly used for solving trust-region subproblems. We propose a method which combines both of these approaches. Using the small-size Lanczos matrix, we apply the More-Sorensen method to a small-size trust-region … Read more

    Additional properties of shifted valiable metric methods.

  • Ladislav Lukšan
  • Jan Vlček
    • Categories Unconstrained Optimization Tags , , , ,

    Some supplements to shifted variable metric or quasi-Newton methods for unconstrained minimization are given, including new limited-memory methods. Global convergence of these methods can be established for convex sufficiently smooth functions. Some encouraging numerical experience is reported. Citation Report No. V899-03, Institute of Computer Scienc, Czech Academy of Sciences, Prague, December 2003 (revised May 2004). … Read more

    New Variable Metric Methods for Unconstrained Minimization Covering the Large-Scale Case

  • Ladislav Lukšan
  • Jan Vlček
    • Categories Nonlinear Optimization, Unconstrained Optimization Tags , ,

    A new family of numerically efficient variable metric or quasi-Newton methods for unconstrained minimization are given, which give simple possibility of adaptation for large-scale optimization. Global convergence of the methods can be established for convex sufficiently smooth functions. Some encouraging numerical experience is reported. Citation Report V876, Institute of Computer Science, AV CR, Pod Vodarenskou … Read more

    Interior-Point Method for Nonlinear Nonconvex Optimization

  • Ladislav Lukšan
  • Jan Vlček
    • Categories Constrained Nonlinear Optimization, Nonlinear Optimization Tags ,

    In this paper, we propose an algorithm for solving nonlinear nonconvex programming problems, which is based on the interior-point approach. Main theoretical results concern direction determination and step-length selection. We split inequality constraints into active and inactive to overcome problems with stability. Inactive constraints are eliminated directly while active constraints are used to define symmetric … Read more

    Nonsmooth Equation Method for Nonlinear Nonconvex Optimization

  • Ladislav Lukšan
  • Jan Vlček
    • Categories Constrained Nonlinear Optimization, Nonlinear Optimization Tags ,

    In this paper, we propose an algorithm for solving nonlinear nonconvex programming problems, which is based on the nonsmooth equation approach. This Algorithm was implemented in the interactive system for universal functional optimization UFO. Results of numerical experiments are reported. Citation Report V844, Institute of Computer Science, AV CR, Pod Vodarenskou Vezi 2, 18207 Praha … Read more