10 citations · 45 across the 35 of their papers we have counts for
5 papers · 1 filter
Note on Steepest Descent Algorithm for Quasi L-convex Function Minimization
Kazuo Murota, Akiyoshi Shioura
We define a class of discrete quasi convex functions, called semi-strictly quasi L-convex functions, and show that the steepest descent algorithm for L-co…
Decomposition of an Integrally Convex Set into a Minkowski Sum of Bounded and Conic Integrally Convex Sets
Kazuo Murota, Akihisa Tamura
Every polyhedron can be decomposed into a Minkowski sum (or vector sum) of a bounded polyhedron and a polyhedral cone. This paper establishes similar statements for some classes of…
Note on Minimization of Quasi M-convex Functions
Kazuo Murota, Akiyoshi Shioura
For a class of discrete quasi convex functions called semi-strictly quasi M-convex functions, we investigate fundamental issues relating to minimization, such as optimal…
Shapley-Folkman-type Theorem for Integrally Convex Sets
Kazuo Murota, Akihisa Tamura
The Shapley-Folkman theorem is a statement about the Minkowski sum of (non-convex) sets, expressing the closeness of the Minkowski sum to convexity in a quantitative manner. This p…
Double-Exponential transformation: A quick review of a Japanese tradition
Kazuo Murota, Takayasu Matsuo
This paper is a short introduction to numerical methods using the double exponential (DE) transformation, such as tanh-sinh quadrature and DE-Sinc approximation. The DE-based metho…