IJPAM: Volume 51, No. 1 (2009)

AND ITS MINIMUM SET OF THE PROPER
CONVEX FUNCTION



Dalian University of Technology
Dalian, 116024, P.R. CHINA


Abstract.The analysis of the -Lagrangian function and its minimum set is critical for giving the
-theory of the proper convex function. Based on that, this paper studies the
-Lagrangian of the proper convex function. We analyze the properties of the
-Lagrangian and give the expression of its subdifferential. Also, we demonstrate the sufficient condition for the nonempty of the minimum set. Further more, we prove the minimum set is outer semicontinuity.
Received: January 22, 2009
AMS Subject Classification: 90C25, 52A41, 26B25, 90C30
Key Words and Phrases: -decomposition,
-Lagrangian, conjugate function, recession function, outer semicontinuity
Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2009
Volume: 51
Issue: 1