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Feasible and noninterior path-following in constrained minimization with low multiplier regularity. (English) Zbl 1121.49030

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.

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)
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