| dc.creator |
Abdulhamid, Idris A. Masoud,
1972-
author
211127 |
|
| dc.creator |
Şahiner, Ahmet,
1970-
thesis advisor
15279 |
|
| dc.creator |
Süleyman Demirel Üniversitesi.
Fen Bilimleri Enstitüsü.
Matematik Anabilim Dalı.
10117
issuing body |
|
| dc.date |
2020. |
|
| dc.identifier |
http://tez.sdu.edu.tr/Tezler/TF04639.pdf |
|
| dc.description |
In the last two decades, deterministic global optimization algorithms have been developed for non convex, nonlinear optimization problems powered by applications spanning science and engineering. The presence of several local minimizers of a non convex objective function implies that global optimization is a significant problem, adding to that moving from a minimizer point to a better one is sometimes a challenge in the search process in addressing continuous global optimization problems. Certain auxiliary functions, namely, filled functions, can be used to address these problems. On the other hand, some algorithms rely on auxiliary function techniques to iteratively decrease extremum points by adding intermediate functional expressions of variables and constraints until each intermediate expression can be externalized with a feasible convex set. In this dissertation, we have developed a new category of auxiliary functions based on the definition of the filled function and the concept of convexity. Namely, (i) we have proposed three new auxiliary functions, which not only preserve the functional features of known traditional functions, but also address difficulties in their computational implementation, for instance, the case of non smoothness. In addition, they are achieving the filled function properties. To demonstrate the applicability of the methods provided, firstly, test functions of 2-50 variables were applied, secondly, we used one of these methods to detect threshold values in images of melanoma in skin cancer. Computational results indicate that the method proposed is strong, reliable, and effective. The best threshold value has been identified for segmentation of the aforementioned lesion. (ii) We introduced a new convex-transforming method, an important class of generalized convex functions which supplies many functional forms often present in non convex problems. The results indicated that the proposed convexification techniques significantly reduced the local minimizers of the given function. Keywords: Global optimization, Nonlinear optimization, Auxiliary function, Globally convex. |
|
| dc.description |
Tez (Doktora) - Süleyman Demirel Üniversitesi, Fen Bilimleri Enstitüsü, Matematik Anabilim Dalı, 2020. |
|
| dc.description |
Kaynakça var. |
|
| dc.description |
In the last two decades, deterministic global optimization algorithms have been developed for non convex, nonlinear optimization problems powered by applications spanning science and engineering. The presence of several local minimizers of a non convex objective function implies that global optimization is a significant problem, adding to that moving from a minimizer point to a better one is sometimes a challenge in the search process in addressing continuous global optimization problems. Certain auxiliary functions, namely, filled functions, can be used to address these problems. On the other hand, some algorithms rely on auxiliary function techniques to iteratively decrease extremum points by adding intermediate functional expressions of variables and constraints until each intermediate expression can be externalized with a feasible convex set. In this dissertation, we have developed a new category of auxiliary functions based on the definition of the filled function and the concept of convexity. Namely, (i) we have proposed three new auxiliary functions, which not only preserve the functional features of known traditional functions, but also address difficulties in their computational implementation, for instance, the case of non smoothness. In addition, they are achieving the filled function properties. To demonstrate the applicability of the methods provided, firstly, test functions of 2-50 variables were applied, secondly, we used one of these methods to detect threshold values in images of melanoma in skin cancer. Computational results indicate that the method proposed is strong, reliable, and effective. The best threshold value has been identified for segmentation of the aforementioned lesion. (ii) We introduced a new convex-transforming method, an important class of generalized convex functions which supplies many functional forms often present in non convex problems. The results indicated that the proposed convexification techniques significantly reduced the local minimizers of the given function. Keywords: Global optimization, Nonlinear optimization, Auxiliary function, Globally convex. |
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| dc.language |
tur |
|
| dc.publisher |
Isparta : Süleyman Demirel Üniversitesi Fen Bilimleri Enstitüsü, |
|
| dc.subject |
Süleyman Demirel Üniversitesi |
|
| dc.title |
Yardımcı fonksiyon metodunda bezier eğrileri yolu ile yönlü arama kullanarak yeni bir global optimizasyon tekniği = A global optimization technique using auxiliary functionmethod in directional search via bezier surface / |
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| dc.type |
text |
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