A Unified Framework of Regularization Methods for Degenerate Non-Linear Optimization Models
Résumé
In this paper, we study three classes of difficult non-linear optimization, problems with complementarity (MPCC), vanishing (MPVC) and cardinality constraints (OMCC). They all have in common degenerate constraints, which fail to satisfy classical constraint qualifications in a generic way. The feasible sets of these problems are non-convex, possibly non-connected, with an empty relative interior. This causes several difficulties in practice. In a recent work (Dussault et al. 2017), we propose a unified framework of methods that consider a regularization-penalization-active set method to solve the MPCC, which possesses the best-known convergence properties. In this paper, we extend this unified framework to MPVC and OMCC and consider some applications on optimal control problems.
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