An Inexact Trust-Region SQP Method with Applications to PDE-Constrained Optimization
M. Heinkenschloss
Department of Computational and Applied Mathematics
Rice University
D. Ridzal
Computational Mathematics and Algorithms
Sandia National Laboratories
In
K. Kunisch, O. Steinbach, and G. Of (eds.),
Numerical Mathematics And Advanced Applications. EUMATH 2007.
Springer-Verlag, Heidelberg, 2008, pp. 613--620.
Abstract
Sequential quadratic programming (SQP) methods compute an approximate
solution of smooth nonlinear programming problems by solving a sequence of quadratic
subproblems. The solution of these subproblems requires the solution of linear systems
in which the system operator involves the constraint Jacobian or its adjoint.
For problems governed by PDEs, the solution of such linear systems is often performed
using iterative solvers, which require carefully selected stopping criteria. These must be
chosen based on the overall progress of the optimization algorithm, in order to ensure
global convergence and avoid unnecessary oversolving of linear systems. We present
an inexact trust-region SQP algorithm with efficient and easily implementable stopping
criteria for iterative linear system solves, followed by applications to PDE-constrained
optimization problems.
Keywords
Sequential quadratic programming, PDE-constrained optimization, iterative solvers,
trust-region