Inexact Sequential Quadratic Programming Methods for the Solution of Inverse Problems Governed by PDEs

Matthias Heinkenschloss

Rice University
Department of Computational and Applied Mathematics
MS-134
Houston TX 77005-1892


Abstract

The numerical solution of inverse problems often leads to large-scale optimization problems. In this talk we discuss the solution of such problems using sequential quadratic programming (SQP) methods. While SQP methods are well established and successfully used for constrained optimization, there are still open issues when SQP subproblems, in particular the linearized constraints, are not solved by direct linear algebra but by iterative methods. Critical issues are the control of inexactness to achieve global convergence of the SQP method and the design of preconditioners for the solution of saddle point SQP subproblems.
In this talk we will first provide the necessary background on SQP methods and motivate the issues that arise when SQP subproblems are solved iteratively. Then we will propose ways to control inexactness to maintain global and local convergence, and we will discuss the construction of preconditioners for the saddle point SQP subproblems. Theoretical results will be supported by applications to inverse problem testexamples.