On a lagrange — Newton method for a nonlinear parabolic boundary control problem∗
- 1 January 1998
- journal article
- research article
- Published by Taylor & Francis in Optimization Methods and Software
- Vol. 8 (3-4) , 225-247
- https://doi.org/10.1080/10556789808805678
Abstract
An optimal control problem governed by the heat equation with nonlinear boundary conditions is considered. The objective functional consists of a quadratic terminal part aifid a quadratic regularization term. On transforming the associated optimality system to! a generalized equation, an SQP method for solving the optimal control problem is related to the Newton method for the generalized equation. In this way, the convergence of tfie SQP method is shown by proving the strong regularity of the optimality system. Aftjer explaining the numerical implementation of the theoretical results some high precision test examples are presentedKeywords
This publication has 17 references indexed in Scilit:
- The numerical solution of a control problem governed by a phase filed modelOptimization Methods and Software, 1997
- Augmented Lagrangian–SQP Methods for Nonlinear Optimal Control Problems of Tracking TypeSIAM Journal on Control and Optimization, 1996
- An SQP method for optimal control of weakly singular Hammerstein integral equationsApplied Mathematics & Optimization, 1996
- Augmented Lagrangian-SQP-Methods in Hilbert Spaces and Application to Control in the Coefficients ProblemsSIAM Journal on Optimization, 1996
- Solution of Optimal Control Problems by a Pointwise Projected Newton MethodSIAM Journal on Control and Optimization, 1995
- Optimality, stability, and convergence in nonlinear controlApplied Mathematics & Optimization, 1995
- The Lagrange-Newton method for nonlinear optimal control problemsComputational Optimization and Applications, 1993
- The lagrange-newton method for infinite-dimensional optimization problemsNumerical Functional Analysis and Optimization, 1990
- Projected Newton Methods for Optimization Problems with Simple ConstraintsSIAM Journal on Control and Optimization, 1982
- On the Fast Solving of Parabolic Boundary Control ProblemsSIAM Journal on Control and Optimization, 1979