Second Order Optimality Conditions and Improved Convergence Results for a Scholtes-type Regularization for a Continuous Reformulation of Cardinality Constrained Optimization Problems

2017/09/05 by Max Bucher, Bucher, Max, Alexandra Schwartz +1
Computer Science · Engineering · Mathematics · #Advanced Optimization Algorithms Research #FOS: Mathematics #Optimization and Control (math.OC) #Optimization and Variational Analysis #Sparse and Compressive Sensing Techniques

paper · pdf · doi:10.48550/arxiv.1709.01368

openalex publication_date 2017/09/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider nonlinear optimization problems with cardinality constraints. Based on a continuous reformulation we introduce second order necessary and sufficient optimality conditions. Under such a second order condition, we can guarantee local uniqueness of M-stationary points. Finally, we use this observation to provide extended local convergence theory for a Scholtes-type relaxation method for cardinality constrained optimization problems, which guarantees the existence and convergence of the iterates under suitable assumptions.

Citations

• Sparsity Constrained Minimization via Mathematical Programming with Equilibrium Constraints

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