Subspace optimization extending the Dog-Leg algorithm (Master thesis)

Ρίζου, Αρσινόη Ειρήνη

The field of « Nonlinear Optimization » has undergone a tremendous development in the last decades with the advent powerful computers. Among the several optimization methodologies, Newton and Quasi-Newton are regarded as the most successful for smooth objective functions with continuous first and second derivatives. Quasi Newton (QN) methods do not need to explicitly calculate the Hessian matrix but use an updating scheme to build the estimation for it over several iterations and need only to calculate the gradient of the objective function. Newton methods on the other hand, require the calculation of both the gradient and the second derivative matrix (Hessian). There are two main approaches currently followed by Newton and QN methods, namely the “Line-search” and the “Trust-region” (also known as Restricted-step). The focus of the present thesis is on “Trust-region” Newton Methods. In particular, the approximate 2-d subspace minimization effected by Powell’s “Dog-Leg”, is replaced by an exact technique that can also treat higher dimensional subspaces. This improves Powell’s Dogleg in two aspects: a) Solves the arising two dimensional optimization subproblem exactly, and b) handles positive-definite, indefinite or negative-definite Hessian matrices on the same footing. The scheme is effective, computationally efficient, and rather simple to implement.
Institution and School/Department of submitter: Πανεπιστήμιο Ιωαννίνων. Πολυτεχνική Σχολή. Τμήμα Μηχανικών Ηλεκτρονικών Υπολογιστών και Πληροφορικής
Subject classification: Αλγόριθμοι υπολογιστών
Keywords: Βελτιστοποίηση υποχώρων,Αλγόριθμος Dog-leg,Dog-Leg,Subspace optimization
Appears in Collections:Διατριβές Μεταπτυχιακής Έρευνας (Masters)

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