Michal Kočvara

Optimization problems with equilibrium constraints and their numerical solution

  • Michal Kočvara
  • Jiri V. Outrata
    • Categories Complementarity and Variational Inequalities, Nonlinear Optimization, Other Topics Tags

    We consider a class of optimization problems with a generalized equation among the constraints. This class covers several problem types like MPEC (Mathematical Programs with Equilibrium Constraints) and MPCC (Mathematical Programs with Complementarity Constraints). We briefly review techniques used for numerical solution of these problems: penalty methods, nonlinear programming (NLP) techniques and Implicit Programming approach … Read more

    PENNON – A Code for Convex Nonlinear and Semidefinite Programming

  • Michal Kočvara
  • Michael Stingl
    • Categories Convex Optimization, Mechanical Engineering, Semi-definite Programming

    We introduce a computer program PENNON for the solution of problems of convex Nonlinear and Semidefinite Programming (NLP-SDP). The algorithm used in PENNON is a generalized version of the Augmented Lagrangian method, originally introduced by Ben-Tal and Zibulevsky for convex NLP problems. We present generalization of this algorithm to convex NLP-SDP problems, as implemented in … Read more

    [PENNON – A Generalized Augmented Lagrangian Methodfor Semidefinite Programming

  • Michal Kočvara
  • Michael Stingl
    • Categories Mechanical Engineering, Second-Order Cone Programming, Semi-definite Programming

    This article describes a generalization of the PBM method by Ben-Tal and Zibulevsky to convex semidefinite programming problems. The algorithm used is a generalized version of the Augmented Lagrangian method. We present details of this algorithm as implemented in a new code PENNON. The code can also solve second-order conic programming (SOCP) problems, as well … Read more