Unit:
Κατεύθυνση Εφαρμοσμένα ΜαθηματικάLibrary of the School of Science
Author:
Stamou Maria-Niki
Supervisors info:
Δρακόπουλος Μιχαήλ,Επίκουρος Καθηγητής ,Τμήμα Μαθηματικών,Εθνικό και Καποδιστριακό Πανεπιστήμιο Αθηνών
Δουγαλής Βασίλειος, Ομ. Καθηγητής, ΕΚΠΑ
Οικονόμου Αντώνιος, Καθηγητής ΕΚΠΑ
Original Title:
Βελτιστοποίηση Συναρτήσεων με Άμεσες Μεθόδους
Translated title:
Function Optimization with direct search methods
Summary:
The thesis has as a reference point an important branch of Numerical Analysis of the optimization function. Our interest focus on methods that do not use techniques of Differential Calculus. The optimization theory and related techniques occupy on a large area of applied mathematics. In this study we examine the issue from both theoretical and computational point of view, with implementation of the relevant algorithms in Matlab. Originally the related symbolism is given and appropriate formalism is proposed for the problem of interest.
The theoretical background is analyzed for direct search optimization methods. As an enlightening example, we analyze in detail the relatively simple method of Compass and give the Matlab code implementation. Then we will examine the other three calculation methods (enhanced Compass, Box and Hooke - Jeeves) that we will use, treating them as special cases of the general theory. For each method, we will provide the Matlab implementation code.
Finally, numerical experiments performed on our four test functions in order to check the effectiveness of procedures, both individually and comparatively. In general, a formulation optimization problem is a problem of finding the best solution from a given set of available options. In the simplest case, our main research goal is to minimize (or maximize) a real function.
Main subject category:
Science
Keywords:
Matlab, Compass Pattern, Box Pattern, Hooke – Jeeves Pattern, Optimization Functions, Case Study, Optimization process.
