Browsing by Author "Kaya, C. Y."
Now showing 1 - 3 of 3
Results Per Page
Sort Options
Item Open Access “Backward differential flow” may not converge to a global minimizer of polynomials(Springer New York LLC, 2015) Arıkan, Orhan; Burachik, R. S.; Kaya, C. Y.We provide a simple counter-example to prove and illustrate that the backward differential flow approach, proposed by Zhu, Zhao and Liu for finding a global minimizer of coercive even-degree polynomials, can converge to a local minimizer rather than a global minimizer. We provide additional counter-examples to stress that convergence to a local minimum via the backward differential flow method is not a rare occurence.Item Open Access Special issue on “Non-linear continuous optimization”(Springer, 2015-02-15) Burachik, R. S.; Kaya, C. Y.; Pınar, M. Ç.This special issue contains five papers dedicated to Nonlinear Continuous Optimization. All these contributions went through a strict and detailed refereeing process, and were revised according to the strict high standards of the journal.Item Open Access Steklov regularization and trajectory methods for univariate global optimization(Springer, 2020) Arıkan, Orhan; Burachik, R. S.; Kaya, C. Y.We introduce a new regularization technique, using what we refer to as the Steklov regularization function, and apply this technique to devise an algorithm that computes a global minimizer of univariate coercive functions. First, we show that the Steklov regularization convexifies a given univariate coercive function. Then, by using the regularization parameter as the independent variable, a trajectory is constructed on the surface generated by the Steklov function. For monic quartic polynomials, we prove that this trajectory does generate a global minimizer. In the process, we derive some properties of quartic polynomials. Comparisons are made with a previous approach which uses a quadratic regularization function. We carry out numerical experiments to illustrate the working of the new method on polynomials of various degree as well as a non-polynomial function.