relaxation method

A novel approach for bilevel programs based on Wolfe duality

  • Yuwei Li
  • Guihua Lin
  • Jin Zhang
  • Xide Zhu
    • Categories Constrained Nonlinear Optimization Tags , , , ,

    This paper considers a bilevel program, which has many applications in practice. To develop effective numerical algorithms, it is generally necessary to transform the bilevel program into a single-level optimization problem. The most popular approach is to replace the lower-level program by its KKT conditions and then the bilevel program can be transformed into a … Read more

    Boundedness Theorems for the Relaxation Method

  • Edoardo Amaldi
  • Raphael Hauser
    • Categories Linear Programming, Polyhedra Tags , , ,

    A classical theorem by Block and Levin says that certain variants of the relaxation method for solving systems of linear inequalities produce bounded sequences of intermediate solutions even when running on inconsistent input data. Using a new approach, we prove a more general version of this result and answer an old open problem of quantifying … Read more