On ℋn+1-convex functions: asymptotic behaviour and subdifferentials. (3rd April 2019)

• Record Type: Journal Article
• Authors: Sheykhi, A.; Doagooei, A. R.
• Is Part Of: Optimization. Volume 68:Number 4(2019)
• Page Start: 801
• Page End: 818
• Publication Date: 2019-04-03
• Subjects: Abstract convexity -- subdifferentials -- minimum type functions -- asymptotic cones -- asymptotic functions; 52A01 -- 26B25; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2018.1547718
• Languages: English
• ISSNs: 0233-1934

Abstract

Abstract: First, we show thatH n + 1, the class of functions defined as the point-wise minimum of n +1 affine functions defined on the Euclidean spaceR n, has the peaking property. Then we characterizeH n + 1 -convex functions by means of asymptotic cones and asymptotic functions. Finally, some conditions in order to guarantee the nonemptiness of subdifferentials ofH n + 1 -convex functions are established.