Regularization method

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

    Two efficient gradient methods with approximately optimal stepsizes based on regularization models for unconstrained optimization

  • Zexian Liu
  • Wangli Chu
  • Hongwei Liu
    • Categories Unconstrained Optimization Tags , , , ,

    It is widely accepted that the stepsize is of great significance to gradient method. Two efficient gradient methods with approximately optimal stepsizes mainly based on regularization models are proposed for unconstrained optimization. More exactly, if the objective function is not close to a quadratic function on the line segment between the current and latest iterates, … Read more