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<p>In this paper, we focus on nonlinear programming problems with cardinality constraints that restrict the number of nonzero components of the decision vector. We start with a straightforward mixed-integer programming reformulation. Inspired by previous papers, the binary restrictions on variables are then relaxed, leading to a large number of stationary points based on the Karush-Kuhn-Tucker optimality conditions. Therefore, we employ so-called binary penalties that penalize the non-binary values in the decision vector. This leads to a&#xa0;desirable reduction in the number of stationary points. In the numerical part, we compare the solution approaches on test instances of a portfolio selection problem.</p>

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Penalty method for cardinality constrained optimization problems with an application in portfolio theory

  • 期刊论文

  • 发表日期：

    2026年6月24日

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  • Martin Branda,
  • Monika Hendrych

摘要

In this paper, we focus on nonlinear programming problems with cardinality constraints that restrict the number of nonzero components of the decision vector. We start with a straightforward mixed-integer programming reformulation. Inspired by previous papers, the binary restrictions on variables are then relaxed, leading to a large number of stationary points based on the Karush-Kuhn-Tucker optimality conditions. Therefore, we employ so-called binary penalties that penalize the non-binary values in the decision vector. This leads to a desirable reduction in the number of stationary points. In the numerical part, we compare the solution approaches on test instances of a portfolio selection problem.