Bengisen Pekmen, M.Sc.
Department of Scientific Computing
August 2009, 85 pages
Supervisor: Bülent Karasözen (Institute of Applied Mathematics, Middle East Technical University, Ankara)
Co-supervisor: Ömür Uğur (Institute of Applied Mathematics, Middle East Technical University, Ankara)
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 derivative 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.
Keywords: trust region method, multivariate interpolation, derivative free optimization, multilevel optimization