Derivative free multilevel optimization methods

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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.