approximate kkt conditions

On the convergence of augmented Lagrangian strategies for nonlinear programming

  • Roberto Andreani
  • A. R. V. Cárdenas
  • Alberto Ramos
  • Ademir A. Ribeiro
  • Leonardo D. Secchin
    • Categories Nonlinear Optimization Tags , , , ,

    Augmented Lagrangian algorithms are very popular and successful methods for solving constrained optimization problems. Recently, the global convergence analysis of these methods have been dramatically improved by using the notion of the sequential optimality conditions. Such conditions are optimality conditions independently of the fulfilment of any constraint qualifications and provide theoretical tools to justify stopping … 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

    Strict Constraint Qualifications and Sequential Optimality Conditions for Constrained Optimization

  • Roberto Andreani
  • José Mario Martínez
  • Alberto Ramos
  • Paulo J. S. Silva
    • Categories Constrained Nonlinear Optimization Tags , , , , , ,

    Sequential optimality conditions for constrained optimization are necessarily satisfied by local minimizers, independently of the fulfillment of constraint qualifications. These conditions support the employment of different stopping criteria for practical optimization algorithms. On the other hand, when an appropriate strict constraint qualification associated with some sequential optimality condition holds at a point that satisfies the … Read more

    A cone-continuity constraint qualification and algorithmic consequences

  • Roberto Andreani
  • José Mario Martínez
  • Alberto Ramos
  • Paulo J. S. Silva
    • Categories Constrained Nonlinear Optimization Tags , , , ,

    Every local minimizer of a smooth constrained optimization problem satisfies the sequential Approximate Karush-Kuhn-Tucker (AKKT) condition. This optimality condition is used to define the stopping criteria of many practical nonlinear programming algorithms. It is natural to ask for conditions on the constraints under which AKKT implies KKT. These conditions will be called Strict Constraint Qualifications … Read more

    A new sequential optimality condition for constrained optimization and algorithmic consequences

  • Roberto Andreani
  • José Mario Martínez
  • Benar Fux Svaiter
    • Categories Nonlinear Optimization Tags , , ,

    Necessary first-order sequential optimality conditions provide adequate theoretical tools to justify stopping criteria for nonlinear programming solvers. These conditions are satisfied by local minimizers of optimization problems independently of the fulfillment of constraint qual- i cations. A new strong sequential optimality condition is introduced in the present paper. A proof that a well established Augmented Lagrangian … Read more