ON DISCRETE HESSIAN MATRIX AND CONVEX EXTENSIBILITY

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概要

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• For functions defined on integer lattice points, discrete versions of the Hessian matrix have been considered in various contexts. In discrete convex analysis, for example certain combinatorial properties of the discrete Hessian matrices are known to characterize M^〓-convex and L^〓-convex functions, which can be extended to convex functions in real variables. The relationship between convex extensibility and discrete Hessian matrices is not fully understood in general, and unfortunately, some vague or imprecise statements have been made in the literature. This note points out that the positive semidefiniteness of the discrete Hessian matrix does not imply nor is implied by convex extensibility of discrete functions.

著者

• Murota Kazuo

  University Of Tokyo

• Moriguchi Satoko

  Advanced Institute Of Industrial Technology

関連論文

• NOTE ON THE CONTINUITY OF M-CONVEX AND L-CONVEX FUNCTIONS IN CONTINUOUS VARIABLES
• ELECTRIC NETWORK CLASSIFIERS FOR SEMI-SUPERVISED LEARNING ON GRAPHS
• ON DISCRETE HESSIAN MATRIX AND CONVEX EXTENSIBILITY

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