first order optimality conditions

Transposition theorems and qualification-free optimality conditions

  • Arnold Neumaier
  • Hermann Schichl
    • Categories Constrained Nonlinear Optimization, Global Optimization Theory, Multi-Criteria Optimization Tags , , , , , , , , , , , ,

    New theorems of the alternative for polynomial constraints (based on the Positivstellensatz from real algebraic geometry) and for linear constraints (generalizing the transposition theorems of Motzkin and Tucker) are proved. Based on these, two Karush-John optimality conditions — holding without any constraint qualification — are proved for single- or multi-objective constrained optimization problems. The first … Read more

    Sharpening the Karush-John optimality conditions

  • Arnold Neumaier
  • Hermann Schichl
    • Categories Constrained Nonlinear Optimization Tags , ,

    A refined version of the Karush-John first order optimality conditions is presented which reduces the number of constraints for which a constraint qualification is needed. This version is a generalization both of the Karush-John conditions and of the first order optimality conditions for concave constraints. ArticleDownload View PDF