Minimizing Increasing Star-shaped Functions Based on Abstract Convexity

Authors:
A. M. Rubinov;M. Yu. Andramonov
Affiliations:
School of Information Technology and Mathematical Sciences, University of Ballarat, Victoria 3353, Australia;School of Information Technology and Mathematical Sciences, University of Ballarat, Victoria 3353, Australia
Venue:
Journal of Global Optimization
Year:
1999

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Abstract

We study a broad class of increasing non-convex functions whose level sets are star shaped with respect to infinity. We show that these functions (we call them ISSI functions) are abstract convex with respect to the set of min-type functions and exploit this fact for their minimization. An algorithm is proposed for solving global optimization problems with an ISSI objective function and its numerical performance is discussed.