Scientific Computing, Applied and Industrial Mathematics (SCAIM) Seminar : Ron Estrin

We describe a penalty function for constrained nonlinear programs, originally proposed by Fletcher (1970). This penalty function is smooth and exact, so that minimizers of the original problem are minimizers of the penalty function for a sufficiently large (but finite) penalty parameter. The main computational kernel required to evaluate this penalty function and its derivatives is solving augmented least-squares like systems. The penalty function can then be efficiently evaluated for problems where good preconditions exist, such as for PDE-constrained optimization problems. We discuss extensions to regularized problems, problems with inequality constraints, and the use of inexact evaluations. We provide some preliminary numerical results on some standard optimization test problems and PDE-constrained problems.

 

 

This is joint work with Michael Friedlander, Dominique Orban and Michael Saunders.