Gabriel Haeser

On the use of Jordan Algebras for improving global convergence of an Augmented Lagrangian method in nonlinear semidefinite programming

  • Roberto Andreani
  • Ellen H. Fukuda
  • Gabriel Haeser
  • Daiana O. Santos
  • Leonardo D. Secchin
    • Categories Nonlinear Optimization, Semi-definite Programming Tags , , , ,

    Jordan Algebras are an important tool for dealing with semidefinite programming and optimization over symmetric cones in general. In this paper, a judicious use of Jordan Algebras in the context of sequential optimality conditions is done in order to generalize the global convergence theory of an Augmented Lagrangian method for nonlinear semidefinite programming. An approximate … Read more

    Constraint Qualifications for Karush-Kuhn-Tucker Conditions in Constrained Multiobjective Optimization

  • Gabriel Haeser
  • Alberto Ramos
    • Categories Constrained Nonlinear Optimization, Nonlinear Optimization Tags , ,

    The notion of a normal cone of a given set is paramount in optimization and variational analysis. In this work, we give a definition of a multiobjective normal cone which is suitable for studying optimality conditions and constraint qualifications for multiobjective optimization problems. A detailed study of the properties of the multiobjective normal cone is … Read more

    On optimality conditions for nonlinear conic programming

  • Roberto Andreani
  • Walter Gómez
  • Gabriel Haeser
  • Alberto Ramos
  • Leonardo M. Mito
    • Categories Constrained Nonlinear Optimization, Linear, Cone and Semidefinite Programming, Nonlinear Optimization Tags , , ,

    Sequential optimality conditions have played a major role in proving stronger global convergence results of numerical algorithms for nonlinear programming. Several extensions have been described in conic contexts, where many open questions have arisen. In this paper, we present new sequential optimality conditions in the context of a general nonlinear conic framework, which explains and … Read more

    On Constraint Qualifications for Second-Order Optimality Conditions Depending on a Single Lagrange Multiplier.

  • Gabriel Haeser
  • Alberto Ramos
    • Categories Constrained Nonlinear Optimization, Nonlinear Optimization Tags , ,

    Second-order optimality conditions play an important role in continuous optimization. In this paper, we present and discuss new constraint qualifications to ensure the validity of some well-known second-order optimality conditions. Our main interest is on second-order conditions that can be associated with numerical methods for solving constrained optimization problems. Such conditions depend on a single … Read more

    Optimality conditions for nonlinear second-order cone programming and symmetric cone programming

  • Roberto Andreani
  • Ellen H. Fukuda
  • Gabriel Haeser
  • Daiana O. Santos
  • Leonardo D. Secchin
    • Categories Linear, Cone and Semidefinite Programming, Nonlinear Optimization, Second-Order Cone Programming Tags , , , ,

    Nonlinear symmetric cone programming (NSCP) generalizes important optimization problems such as nonlinear programming, nonlinear semidefinite programming and nonlinear second-order cone programming (NSOCP). In this work, we present two new optimality conditions for NSCP without constraint qualifications, which implies the Karush-Kuhn-Tucker conditions under a condition weaker than Robinson’s constraint qualification. In addition, we show the relationship … Read more

    An Augmented Lagrangian algorithm for nonlinear semidefinite programming applied to the covering problem

  • Ernesto G. Birgin
  • Walter Gómez
  • Gabriel Haeser
  • Leonardo M. Mito
  • Daiana O. Santos
    • Categories Constrained Nonlinear Optimization, Convex Optimization, Semi-definite Programming Tags , , ,

    In this work we present an Augmented Lagrangian algorithm for nonlinear semidefinite problems (NLSDPs), which is a natural extension of its consolidated counterpart in nonlinear programming. This method works with two levels of constraints; one that is penalized and other that is kept within the subproblems. This is done in order to allow exploiting the … Read more

    An Augmented Lagrangian Method for Quasi-Equilibrium Problems

  • Luís Felipe Bueno
  • Gabriel Haeser
  • Felipe Lara
  • Frank Navarro Rojas
    • Categories Nonlinear Optimization

    In this paper, we propose an Augmented Lagrangian algorithm for solving a general class of possible non-convex problems called quasi-equilibrium problems (QEPs). We define an Augmented Lagrangian bifunction associated with QEPs, introduce a secondary QEP as a measure of infeasibility and we discuss several special classes of QEPs within our theoretical framework. For obtaining global … Read more

    Towards an efficient Augmented Lagrangian method for convex quadratic programming

  • Luís Felipe Bueno
  • Gabriel Haeser
  • Luiz-Rafael Santos
    • Categories Constrained Nonlinear Optimization, Linear Programming, Quadratic Programming Tags , , , ,

    Interior point methods have attracted most of the attention in the recent decades for solving large scale convex quadratic programming problems. In this paper we take a different route as we present an augmented Lagrangian method for convex quadratic programming based on recent developments for nonlinear programming. In our approach, box constraints are penalized while … Read more

    New sequential optimality conditions for mathematical problems with complementarity constraints and algorithmic consequences

  • Roberto Andreani
  • Gabriel Haeser
  • Paulo J. S. Silva
  • Leonardo D. Secchin
    • Categories Nonlinear Optimization

    In recent years, the theoretical convergence of iterative methods for solving nonlinear constrained optimization problems has been addressed using sequential optimality conditions, which are satisfied by minimizers independently of constraint qualifications (CQs). Even though there is a considerable literature devoted to sequential conditions for standard nonlinear optimization, the same is not true for Mathematical Problems … Read more

    Optimality conditions and global convergence for nonlinear semidefinite programming

  • Roberto Andreani
  • Gabriel Haeser
  • Daiana O. Santos
    • Categories Nonlinear Optimization, Semi-definite Programming Tags , , ,

    Sequential optimality conditions have played a major role in unifying and extending global convergence results for several classes of algorithms for general nonlinear optimization. In this paper, we extend theses concepts for nonlinear semidefinite programming. We define two sequential optimality conditions for nonlinear semidefinite programming. The first is a natural extension of the so-called Approximate-Karush-Kuhn-Tucker … Read more