cardinality constraint

A General Penalty-Method and a General Regularization-Method for Cardinality-Constrained Optimization Problems

  • Felix P. Broesamle
    • Categories Complementarity and Variational Inequalities, Constrained Nonlinear Optimization, Nonlinear Optimization Tags , , , , ,

    We consider cardinality-constrained optimization problems (CCOPs), which are general nonlinear programs with an additional constraint limiting the number of nonzero continuous variables. The continuous reformulation of CCOPs involves complementarity constraints, which pose significant theoretical and computational challenges. To address these difficulties, we propose and analyze two numerical solution approaches: a general penalty method and a … Read more

    Recoverable Robust Cardinality Constrained Maximization with Commitment of a Submodular Function

  • Sabine Münch
  • Sven de Vries
    • Categories Approximation Algorithms, Combinatorial Optimization Tags , , ,

    We consider a game-theoretic variant of maximizing a monotone increasing, submodular function under a cardinality constraint. Initially, a solution to this classical problem is determined. Subsequently, a predetermined number of elements from the ground set, not necessarily contained in the initial solution, are deleted, potentially reducing the solution’s cardinality. If any deleted elements were part … Read more

    Tighter yet more tractable relaxations and nontrivial instance generation for sparse standard quadratic optimization

  • Immanuel M. Bomze
  • Bo Peng
  • Yuzhou Qiu
  • E. Alper Yildirim
    • Categories (Mixed) Integer Nonlinear Programming, Cone Programming, Semi-definite Programming Tags , , , ,

    The Standard Quadratic optimization Problem (StQP), arguably the simplest among all classes of NP-hard optimization problems, consists of extremizing a quadratic form (the simplest nonlinear polynomial) over the standard simplex (the simplest polytope/compact feasible set). As a problem class, StQPs may be nonconvex with an exponential number of inefficient local solutions. StQPs arise in a … Read more

    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