IJPAM: Volume 57, No. 1 (2009)

ALGORITHMS FOR MIXED CONVEXITY AND
OPTIMIZATION OF 2-SMOOTH MIXED
CONVEX FUNCTIONS

Emre Tokgöz
Department of Mathematics
University of Oklahoma
601 Elm Ave., Room 423, Norman, OK, 73019, USA
e-mail: Emre.Tokgoz-1@ou.edu


Abstract.In the queueing systems theory, there are systems where the convexity and minimization of functions with real and integer variables are considered. The developed theories on convexity of both real variable and integer variable functions are not enough to give a precise answer to the convexity of 2-smooth mixed functions. Tokgöz, Maalouf and Kumin [#!2!#] introduced a mixed Hessian matrix that is useful to check the convexity of 2-smooth mixed functions and proved minimization results for 2-smooth mixed convex functions. In this paper, an algorithm to find the mixed convexity of 2-smooth mixed functions is given with an application to an example. An algorithm to find the global minimum value of 2-smooth mixed convex functions is also given.

Received: October 10, 2009

AMS Subject Classification: 26B25, 52A41, 90C30

Key Words and Phrases: discrete convex function, real convex function, Hessian matrix, optimization, algorithm

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2009
Volume: 57
Issue: 1