Tröltzsch, Fredi : On the Lagrange-Newton-SQP Method for the Optimal Control of Semilinear Parabolic Equations

Author(s) :

Tröltzsch, Fredi

Title :

On the Lagrange-Newton-SQP Method for the Optimal Control of Semilinear Parabolic Equations

Electronic source :

[gzipped ps-file] 84 kB

Preprint series

Technische Universität Chemnitz, Fakultät für Mathematik (Germany). Preprint 98-13, 1998

Mathematics Subject Classification :

49J20 [ Optimal control problems with PDE (existence) ]

49M15 [ Methods of Newton-Raphson, Galerkin and Ritz types ]

65K10 [ Optimization techniques (numerical methods) ]

49K20 [ Optimal control problems with PDE (nec./ suff.) ]

Abstract :

A class of Lagrange-Newton-SQP methods is investigated for optimal control problems governed by semilinear parabolic initial- boundary value problems. Distributed and boundary controls are given, restricted by pointwise upper and lower bounds. The convergence of the method is discussed in appropriate Banach spaces. Based on a weak second order sufficient optimality condition for the reference solution, local quadratic convergence is proved. The proof is based on the theory of Newton methods for generalized equations in Banach spaces.

Keywords :

optimal control, parabolic equation, semilinear equation, sequential quadratic programming, Lagrange-Newton method, convergence analysis

Language :

english

Publication time :

7/1998