IJPAM: Volume 56, No. 1 (2009)

MIXED T-, T$^{\ast}$-CONVEX FUNCTIONS AND
THEIR CORRESPONDING MIXED HESSIAN MATRICES

Emre Tokgöz
Department of Mathematics
University of Oklahoma
Norman, OK 73019, USA
e-mail: [email protected]


Abstract.Many minimization problems include functions with integer variables or a combination of integer and real variables.

L and L$^{\natural}$-convex functions are integer functions with the property that any local minimum is a global minimum. In this paper, the definition of these functions is extended to include real variables in the domain. Mixed Hessian matrices are defined for T and T$^{\ast}$-convex functions with properties similar to those of the Hessian matrix for real variables.

Received: August 28, 2009

AMS Subject Classification: 26B25

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

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2009
Volume: 56
Issue: 1