Thesis Type: Postgraduate
Institution Of The Thesis: Orta Doğu Teknik Üniversitesi, Institute of Applied Mathematics, Scientific Computing, Turkey
Approval Date: 2009
Student: BENGİSEN PEKMEN
Co-Supervisor: BÜLENT KARASÖZEN, ÖMÜR UĞUR
Abstract:Derivative free optimization algorithms are implementations of trust region based derivative-free methods using multivariate polynomial interpolation. These are designed to minimize smooth functions whose derivatives are not available or costly to compute. The trust region based multilevel optimization algorithms for solving large scale unconstrained optimization problems resulting by discretization of partial differential equations (PDEs), make use of different discretization levels to reduce the computational cost. In this thesis, a derivative free multilevel optimization algorithm is derived and its convergence behavior is analyzed. The effectiveness of the algorithms is demonstrated on a shape optimization problem.