GLOBAL OPTIMIZATION OF THE DIFFERENCE OF TWO INCREASING PLUS-CONVEX-ALONG-RAYS FUNCTIONS

doi:10.1007/s10473-020-0615-6

Acta mathematica scientia,Series B ›› 2020, Vol. 40 ›› Issue (6): 1849-1873.doi: 10.1007/s10473-020-0615-6

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GLOBAL OPTIMIZATION OF THE DIFFERENCE OF TWO INCREASING PLUS-CONVEX-ALONG-RAYS FUNCTIONS

H. SHAHRIARIPOUR¹, H. MOHEBI²

1. Department of Mathematics, Graduate University of Advanced Technology, Kerman, Iran;
2. Department of Mathematics and Mahani Mathematical Research Center, Shahid Bahonar University of Kerman, P. O. Box:76169133, Postal Code:7616914111, Kerman, Iran

Received:2019-06-06 Revised:2020-07-17 Online:2020-12-25 Published:2020-12-30
Contact: H. MOHEBI,E-mail:hmohebi@uk.ac.ir E-mail:hmohebi@uk.ac.ir
Supported by:
The second author was partially supported by the Mahani Mathematical Research Center, Iran, grant no:97/3267.

Abstract

Abstract: The theory of increasing and convex-along-rays (ICAR) functions defined on a convex cone in a real locally convex topological vector space X was already well developed. In this paper, we first examine abstract convexity of increasing plus-convex-along-rays (IPCAR) functions defined on a real normed linear space X. We also study, for this class of functions, some concepts of abstract convexity, such as support sets and subdifferentials. Finally, as an application, we characterize the maximal elements of the support set of strictly IPCAR functions and give optimality conditions for the global minimum of the difference between two IPCAR functions.

Key words: increasing plus-convex-along-rays function, support set, maximal element, global minimum, DC-function

CLC Number:

90C46

H. SHAHRIARIPOUR, H. MOHEBI. GLOBAL OPTIMIZATION OF THE DIFFERENCE OF TWO INCREASING PLUS-CONVEX-ALONG-RAYS FUNCTIONS[J].Acta mathematica scientia,Series B, 2020, 40(6): 1849-1873.

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GLOBAL OPTIMIZATION OF THE DIFFERENCE OF TWO INCREASING PLUS-CONVEX-ALONG-RAYS FUNCTIONS

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