Gabriel Haeser

Primal-dual relationship between Levenberg-Marquardt and central trajectories for linearly constrained convex optimization

  • Roger Behling
  • Clóvis Caesar Gonzaga
  • Gabriel Haeser
    • Categories Convex Optimization, Quadratic Programming Tags , , , , , ,

    We consider the minimization of a convex function on a compact polyhedron defined by linear equality constraints and nonnegative variables. We define the Levenberg-Marquardt (L-M) and central trajectories starting at the analytic center and using the same parameter, and show that they satisfy a primal-dual relationship, being close to each other for large values of … Read more

    Two new weak constraint qualifications and applications

  • Roberto Andreani
  • Gabriel Haeser
  • Paulo J. S. Silva
  • María Laura Schuverdt
    • Categories Constrained Nonlinear Optimization Tags , , ,

    We present two new constraint qualifications (CQ) that are weaker than the recently introduced Relaxed Constant Positive Linear Depen- dence (RCPLD) constraint qualification. RCPLD is based on the assump- tion that many subsets of the gradients of the active constraints preserve positive linear dependence locally. A major open question was to identify the exact set … Read more

    A relaxed constant positive linear dependence constraint qualification and applications

  • Roberto Andreani
  • Gabriel Haeser
  • Paulo J. S. Silva
  • María Laura Schuverdt
    • Categories Constrained Nonlinear Optimization Tags , ,

    In this work we introduce a relaxed version of the constant positive linear dependence constraint qualification (CPLD) that we call RCPLD. This development is inspired by a recent generalization of the constant rank constraint qualification from Minchenko and Stakhovski that was called RCR. We show that RCPLD is enough to ensure the convergence of an … Read more

    On approximate KKT condition and its extension to continuous variational inequalities

  • Gabriel Haeser
  • María Laura Schuverdt
    • Categories Nonlinear Optimization Tags , ,

    In this work we introduce a necessary natural sequential Approximate-Karush-Kuhn-Tucker (AKKT) condition for a point to be a solution of a continuous variational inequality problem without constraint quali cations, and we prove its relation with the Approximate Gradient Projection condition (AGP) of Garciga-Otero and Svaiter. We also prove that a slight variation of the AKKT condition … Read more

    On the global convergence of interior-point nonlinear programming algorithms

  • Gabriel Haeser
    • Categories Constrained Nonlinear Optimization, Nonlinear Optimization

    Carathéodory’s lemma states that if we have a linear combination of vectors in R^n, we can rewrite this combination using a linearly independent subset. This result has been successfully applied in nonlinear optimization in many contexts. In this work we present a new version of this celebrated theorem, in which we obtained new bounds for … Read more

    On sequential optimality conditions for smooth constrained optimization

  • Roberto Andreani
  • Gabriel Haeser
  • José Mario Martínez
    • Categories Nonlinear Optimization Tags , , ,

    Sequential optimality conditions provide adequate theoretical tools to justify stopping criteria for nonlinear programming solvers. Approximate KKT and Approximate Gradient Projection conditions are analyzed in this work. These conditions are not necessarily equivalent. Implications between different conditions and counter-examples will be shown. Algorithmic consequences will be discussed. ArticleDownload View PDF