cardinality constraint

On the weakest constraint qualification for sharp local minimizers

  • Oliver Stein
  • Maximilian Volk
    • Categories Constrained Nonlinear Optimization Tags , , , ,

    The sharp local minimality of feasible points of nonlinear optimization problems is known to possess a characterization by a strengthened version of the Karush-Kuhn-Tucker conditions, as long as the Mangasarian-Fromovitz constraint qualification holds. This strengthened condition is not easy to check algorithmically since it involves the topological interior of some set. In this paper we … Read more

    Strong valid inequalities for a class of concave submodular minimization problems under cardinality constraints

  • Simge Küçükyavuz
  • Qimeng Yu
    • Categories (Mixed) Integer Linear Programming, Branch and Cut Algorithms, Polyhedra Tags , ,

    We study the polyhedral convex hull structure of a mixed-integer set which arises in a class of cardinality-constrained concave submodular minimization problems. This class of problems has an objective function in the form of $f(a^\top x)$, where $f$ is a univariate concave function, $a$ is a non-negative vector, and $x$ is a binary vector of … Read more