Discrete Hessian Matrix for L-Convex Functions

Satoko MORIGUCHI  Kazuo MUROTA  

Publication
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E88-A   No.5   pp.1104-1108
Publication Date: 2005/05/01
Online ISSN: 
DOI: 10.1093/ietfec/e88-a.5.1104
Print ISSN: 0916-8508
Type of Manuscript: Special Section PAPER (Special Section on Discrete Mathematics and Its Applications)
Category: 
Keyword: 
discrete optimization,  discrete convex function,  Hessian matrix,  local quadratic expansion,  

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Summary: 
L-convex functions are nonlinear discrete functions on integer points that are computationally tractable in optimization. In this paper, a discrete Hessian matrix and a local quadratic expansion are defined for L-convex functions. We characterize L-convex functions in terms of the discrete Hessian matrix and the local quadratic expansion.