squared slack variables

A note on the squared slack variables technique for nonlinear optimization

  • Ellen H. Fukuda
  • Masao Fukushima
    • Categories Constrained Nonlinear Optimization Tags , , ,

    In constrained nonlinear optimization, the squared slack variables can be used to transform a problem with inequality constraints into a problem containing only equality constraints. This reformulation is usually not considered in the modern literature, mainly because of possible numerical instabilities. However, this argument only concerns the development of algorithms, and nothing stops us in … Read more

    Optimality conditions for nonlinear semidefinite programming via squared slack variables

  • Ellen H. Fukuda
  • Bruno F. Lourenço
  • Masao Fukushima
    • Categories Nonlinear Optimization, Semi-definite Programming Tags , , ,

    In this work, we derive second-order optimality conditions for nonlinear semidefinite programming (NSDP) problems, by reformulating it as an ordinary nonlinear programming problem using squared slack variables. We first consider the correspondence between Karush-Kuhn-Tucker points and regularity conditions for the general NSDP and its reformulation via slack variables. Then, we obtain a pair of “no-gap” … Read more