quasi-normality

On the boundedness of multipliers in augmented Lagrangian methods for mathematical programs with complementarity constraints

  • Roberto Andreani
  • Mariana da Rosa
  • Leonardo D. Secchin
    • Categories Nonlinear Optimization Tags , , ,

    In this paper, we analyze augmented Lagrangian (AL) methods for mathematical programs with complementarity constraints (MPCCs), with emphasis on a variant that reformulates the complementarity constraints by slack variables and preserves them explicitly in the subproblems instead of penalizing them. Motivated by recent developments in nonlinear programming, we study quasi-normality-type constraint qualifications tailored to this … Read more

    On enhanced KKT optimality conditions for smooth nonlinear optimization

  • Roberto Andreani
  • María Laura Schuverdt
  • Leonardo D. Secchin
    • Categories Nonlinear Optimization Tags , , , ,

    The Fritz-John (FJ) and KKT conditions are fundamental tools for characterizing minimizers and form the basis of almost all methods for constrained optimization. Since the seminal works of Fritz John, Karush, Kuhn and Tucker, FJ/KKT conditions have been enhanced by adding extra necessary conditions. Such an extension was initially proposed by Hestenes in the 1970s … Read more