Maximal elements of sub-topical functions with applications to global optimization

Document Type : ORO2013

Author

Department of Applied Mathematics‎, ‎Shahid Bahonar University‎ ‎of Kerman‎, ‎Kerman‎, ‎Iran.

Abstract

We study the support sets of sub-topical functions‎ ‎and investigate their maximal elements in order to establish a necessary and sufficient condition‎ ‎for the global minimum of the difference of two sub-topical functions‎.

Keywords

Main Subjects


A. R. Doagooei, Sub-topical functions and plus-co-radiant sets, Optimization 65 (2016), no. 1, 107--119.
A. R. Doagooei and H. Mohebi, Optimization of the difference of topical functions, J. Global Optim. 57 (2013), no. 4, 1349--1358.
S. Gaubert and J. Gunawardena, A non-linear hierarchy for discrete event dynamical systems, Proc. 4th Workshop on discrete event systems, Calgiari, Technical Report HPL-BRIMS-98-20, Hewlett-Packard Labs. 1998.
B. M. Glover and A. M. Rubinov, Toland-Singer formula cannot distinguish a global minimizer from a choice of stationary points, Numer. Funct. Anal. Optim. 20 (1999), no. 1-2, 99--119.
J. Gunawardena, An Introduction to Idempotency, Cambridge Univ. Press, Cambridge, 1998.
J. Gunawardena, From max-plus algebra to non-expansive mappings: a non-linear theory for discrete event systems, Theoretical Computer Science, Technical Report HPL- BRIMS-99-07, Hewlett-Packard Labs. 1999.
A. Rubinov, Abstract Convexity and Global Optimization, Kluwer Academic Publishers, 2000.
A. M. Rubinov and M. Y. Andramonov, Minimizing increasing star-shaped functions based on abstract convexity, J. Global Optim. 15 (1999), no. 1, 19--39.
A. M. Rubinov and B. M. Glover, Increasing convex-along-rays functions with applications to global optimization, J. Optim. Theory Appl. 102 (1999), no. 3, 615--642.
A. M. Rubinov and I. Singer, Topical and sub-topical functions, downward sets and abstract convexity, Optimization 50 (2001) 307--351.
A. M. Rubinov and A. Uderzo, On global optimality conditions via separation functions, J. Optim. Theory Appl. 109 (2001), no. 2, 345--370.
A. M. Rubinov and A. Vladimirov, Convex-along-rays functions and star-shaped sets, Numer. Funct. Anal. Optim. 19 (1998), no. 5-6, 593--613.
I. Singer, Abstract Convex Analysis, John Wiley & Sons, New York, 1997.
I. Singer, Further application of the additive min-type coupling function, Optimization 51 (2002), no. 3, 471--485.
J. F. Toland, Duality in nonconvex optimization, J. Math. Anal. Appl. 66 (1978) 399--415.