Introduction to convex optimization

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Tanoumand, Neda (2019) Introduction to convex optimization. [Thesis]

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Abstract

In this thesis, we touched upon the concept of convexity which is one of the essential topics in optimization. There exist many real world problems that mathematically modelling these problems and trying to solve them are the focus point of many researchers. Many algorithms are proposed for solving such problems. Almost all proposed methods are very efficient when the modelled problems are convex. Therefore, convexity plays an important role in solving those problems. There are many techniques that researchers use to convert a non-convex model to a convex one. Also, most of the algorithms that are suggested for solving non-convex problems try to utilize the notions of convexity in their procedures. In this work, we begin with important definitions and topics regarding convex sets and function. Next, we will introduce optimization problems in general, then, we will discuss convex optimization problems and give important definitions in relation with the topic. Furthermore, we will touch upon Linear Programming which is one of the most famous and useful cases of Convex Optimization problems. Finally, we will discuss the Generalized Inequalities and their application in vector optimization problems
Item Type: Thesis
Uncontrolled Keywords: Convexity. -- Convex sets. -- Convex functions. -- Convex optimization. -- Linear programming. -- Vector Optimization. -- Dışbükeylik.-- Dışbükey kümeler. -- Dışbükey fonksiyonlar. -- Dışbükey optimizasyon. -- Doğrusal programlama. -- Vektör optimizasyon.
Subjects: Q Science > QA Mathematics
Divisions: Faculty of Engineering and Natural Sciences > Basic Sciences > Mathematics
Faculty of Engineering and Natural Sciences
Depositing User: IC-Cataloging
Date Deposited: 23 Sep 2019 16:17
Last Modified: 26 Apr 2022 10:31
URI: https://research.sabanciuniv.edu/id/eprint/39251

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