function approximation

Polynomial argmin for recovery and approximation of multivariate discontinuous functions

  • Didier Henrion
  • Milan Korda
  • Jean-Bernard Lasserre
    • Categories Basic Sciences Applications, Linear, Cone and Semidefinite Programming, Semi-definite Programming Tags , ,

    We propose to approximate a (possibly discontinuous) multivariate function f(x) on a compact set by the partial minimizer arg min_y p(x,y) of an appropriate polynomial p whose construction can be cast in a univariate sum of squares (SOS) framework, resulting in a highly structured convex semidefinite program. In a number of non-trivial cases (e.g. when … Read more

    Solving a Class of Cut-Generating Linear Programs via Machine Learning

  • Danial Davarnia
  • Atefeh Rajabalizadeh
    • Categories Branch and Cut Algorithms, Data-Mining, Linear Programming Tags , , , ,

    Cut-generating linear programs (CGLPs) play a key role as a separation oracle to produce valid inequalities for the feasible region of mixed-integer programs. When incorporated inside branch-and-bound, the cutting planes obtained from CGLPs help to tighten relaxations and improve dual bounds. However, running the CGLPs at the nodes of the branch-and-bound tree is computationally cumbersome … Read more