The conjugate of the pointwise maximum of two convex functions revisited
- 107 Downloads
In this paper we use the tools of the convex analysis in order to give a suitable characterization for the epigraph of the conjugate of the pointwise maximum of two proper, convex and lower semicontinuous functions in a normed space. By using this characterization we obtain, as a natural consequence, the formula for the biconjugate of the pointwise maximum of two functions, provided the so-called Attouch–Brézis regularity condition holds.
KeywordsPointwise maximum Conjugate functions Attouch–Brézis regularity condition
AMS Subject Classification49N15 90C25 90C46
Unable to display preview. Download preview PDF.
- 1.Attouch H. and Brézis H. (1986). Duality for the sum of convex functions in general Banach spaces. In: Barroso, J.A. (eds) Aspects of Mathematics and Its Applications, pp 125–133. North-Holland, Mathematical Library, Amsterdam Google Scholar
- 2.Boţ, R.I., Grad, S.M.: Regularity conditions for formulae of biconjugate functions (submitted)Google Scholar
- 3.Boţ R.I. and Wanka G. (2006). A weaker regularity condition for subdifferential calculus and Fenchel duality in infinite dimensional spaces. In: Nonlinear Anal. Theory Methods Appl. 64(12): 1367–1381 Google Scholar
- 4.Burachik R.S. and Jeyakumar V. (2005). A dual condition for the convex subdifferential sum formula with applications. J. Convex Anal. 12(2): 279–290 Google Scholar
- 7.Zălinescu C. (2002). Convex analysis in general vector spaces. World Scientific, Singapore Google Scholar