On Steepest Descent Algorithms for Discrete Convex Functions

Authors:
Kazuo Murota
Affiliations:
-
Venue:
SIAM Journal on Optimization
Year:
2003

Citing 0
Cited 6

Note on Multimodularity and L-Convexity

Mathematics of Operations Research
Minimizing total variation for field splitting with feathering in intensity-modulated radiation therapy

FAW'10 Proceedings of the 4th international conference on Frontiers in algorithmics
Appointment Scheduling with Discrete Random Durations

Mathematics of Operations Research
A fast solver for truncated-convex priors: quantized-convex split moves

EMMCVPR'11 Proceedings of the 8th international conference on Energy minimization methods in computer vision and pattern recognition
Submodularity on a tree: unifying L-convex and bisubmodular functions

MFCS'11 Proceedings of the 36th international conference on Mathematical foundations of computer science
New algorithms for convex cost tension problem with application to computer vision

Discrete Optimization

Quantified Score

Hi-index	0.00

Visualization

Abstract

This paper investigates the complexity of steepest descent algorithms for two classes of discrete convex functions: M-convex functions and L-convex functions. Simple tie-breaking rules yield complexity bounds that are polynomials in the dimension of the variables and the size of the effective domain. Combining the present results with a standard scaling approach leads to an efficient algorithm for L-convex function minimization.