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  1. 2 Acta Physica Polonica A

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  1. 1 2016

  2. 1 2015

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  1. 2 Tezel Özturan A.

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On an Application of Generalized Semi-Infinite Optimization

100%
Tezel Özturan A.
Acta Physica Polonica A
|
2016
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vol. 130
|
issue 1
14-16
EN
Generalized semi-infinite optimization problems are optimization problems having infinitely many constraints. In addition, the infinite index set depends on the decision variable of optimization. In this study, as an application of generalized semi-infinite optimization problems a type of design centering problems is considered. In a general design centering problem some measure of a parametrized body is maximized under the constraint that parametrized body is inscribed in a fixed body. In this study, diamond cutting problem is considered as a type of design centering problems. Here the aim is to maximize the volume of a round cut diamond from functional approximation of a rough irregularly shaped gemstone. First of all, the problem is converted to a generalized semi-infinite optimization problem, then corresponding first order optimality conditions are obtained. Several numerical examples are presented by solving reformulated Karush-Kuhn-Tucker optimality conditions with semismooth Newton method. The advantage of the method is that a linear system of equations has to be solved in each iteration.
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Solving Generalized Semi-Infinite Programming Problems with a Trust Region Method

100%
Tezel Özturan A.
Acta Physica Polonica A
|
2015
|
vol. 128
|
issue 2B
B-93-B-96
EN
In this paper, a trust region method for generalized semi-infinite programming problems is presented. The method is based on [O. Yi-gui, "A filter trust region method for solving semi-infinite programming problems", J. Appl. Math. Comput. 29, 311 (2009)]. We transformed the method from standard to generalized semi-infinite programming problems. The semismooth reformulation of the Karush-Kuhn-Tucker conditions using nonlinear complementarity functions is used. Under some standard regularity condition from semi-infinite programming, the method is convergent globally and superlinearly. Numerical examples from generalized semi-infinite programming illustrate the performance of the proposed method.
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