Hintermüller, M.; Kunisch, K. Feasible and noninterior path-following in constrained minimization with low multiplier regularity. (English) Zbl 1121.49030 SIAM J. Control Optim. 45, No. 4, 1198-1221 (2006). Summary: Primal-dual path-following methods for constrained minimization problems in function space with low multiplier regularity are introduced and analyzed. Regularity properties of the path are proved. The path structure allows us to define approximating models, which are used for controlling the path parameter in an iterative process for computing a solution of the original problem. The Moreau-Yosida regularized subproblems of the new path-following technique are solved efficiently by semismooth Newton methods. The overall algorithmic concept is provided, and numerical tests (including a comparison with primal-dual path-following interior point methods) for state constrained optimal control problems show the efficiency of the new concept. Cited in 1 ReviewCited in 50 Documents MSC: 49M15 Newton-type methods 49M37 Numerical methods based on nonlinear programming 65K05 Numerical mathematical programming methods 90C33 Complementarity and equilibrium problems and variational inequalities (finite dimensions) (aspects of mathematical programming) 49N60 Regularity of solutions in optimal control 49N15 Duality theory (optimization) Keywords:active set strategy; Moreau-Yosida regularization; path-following methods; primal-dual methods; semismooth Newton methods PDFBibTeX XMLCite \textit{M. Hintermüller} and \textit{K. Kunisch}, SIAM J. Control Optim. 45, No. 4, 1198--1221 (2006; Zbl 1121.49030) Full Text: DOI