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arXiv · 1809.04530

Steklov Regularization and Trajectory Methods for Univariate Global Optimization

Orhan Arıkan·Regina S. Burachik·C. Yalçın Kaya
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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.

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Orhan Arıkan, Regina S. Burachik, C. Yalçın Kaya. 2018-09-09. Steklov Regularization and Trajectory Methods for Univariate Global Optimization. https://arxiv.org/abs/1809.04530

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