Gabriel Haeser

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

    New Constraint Qualifications with Second-Order Properties in Nonlinear Optimization

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

    In this paper we present and discuss new constraint qualifications to ensure the validity of well known second-order properties in nonlinear optimization. Here, we discuss conditions related to the so-called basic second-order condition, where a new notion of polar pairing is introduced in order to replace the polar operation, useful in the first-order case. We … Read more

    Optimality Conditions and Constraint Qualifications for Generalized Nash Equilibrium Problems and their Practical Implications

  • Luís Felipe Bueno
  • Gabriel Haeser
  • Frank Navarro Rojas
    • Categories Constrained Nonlinear Optimization, Game Theory Tags , , , ,

    Generalized Nash Equilibrium Problems (GNEPs) are a generalization of the classic Nash Equilibrium Problems (NEPs), where each player’s strategy set depends on the choices of the other players. In this work we study constraint qualifications and optimality conditions tailored for GNEPs and we discuss their relations and implications for global convergence of algorithms. Surprisingly, differently … Read more

    On the behavior of Lagrange multipliers in convex and non-convex infeasible interior point methods

  • Gabriel Haeser
  • Yinyu Ye
  • Oliver Hinder
    • Categories Nonlinear Optimization Tags , , , ,

    This paper analyzes sequences generated by infeasible interior point methods. In convex and non-convex settings, we prove that moving the primal feasibility at the same rate as complementarity will ensure that the Lagrange multiplier sequence will remain bounded, provided the limit point of the primal sequence has a Lagrange multiplier, without constraint qualification assumptions. We … Read more