Steklov regularization and trajectory methods for univariate global optimization

Orhan Arıkan (), Regina S. Burachik () and C. Yalçın Kaya ()
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Orhan Arıkan: Bilkent University
Regina S. Burachik: University of South Australia
C. Yalçın Kaya: University of South Australia

Journal of Global Optimization, 2020, vol. 76, issue 1, No 5, 120 pages

Abstract: Abstract 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.

Keywords: Global optimization; Mean filter; Steklov smoothing; Steklov regularization; Scale–shift invariance; Trajectory methods (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1007/s10898-019-00837-3

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