Introduction to Discrete Convex Analysis

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Title: Introduction to Discrete Convex Analysis
Author: Murota, Kazuo
Abstract: Discrete convex analysis is a theory that aims at a discrete analogue of convex analysis for nonlinear discrete optimization. Technically it is a nonlinear generalization of matroid/submodular function theory; matroids are generalized to M-convex functions and submodular set functions to L-convex function.This talk consists of two parts: In the first part fundamental concepts and theorems in discrete convex analysis are explained with reference to familiar combinatorial optimization problems like minimum spanning tree, shortest path, and matching. In view of the recent development in submodular function maximization, minimization and maximization algorithms in discrete convex analysis are explained in the second part of the talk. In particular, M-natural concave functions form a subclass of submodular functions that can be maximized in polynomial time.
Description: Presented at the Georgia Tech Algorithms & Randomness Center workshop: Modern Aspects of Submodularity, March 19-22, 2012. Runtime: 48:19 minutes.
Type: Lecture
Date: 2012-03-19
Contributor: Georgia Institute of Technology. School of Computer Science
University of Tokyo
Publisher: Georgia Institute of Technology
Subject: Discrete convexity
Discrete convex functions

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