Note on Steepest Descent Algorithm for Quasi L${}^{♮}$-convex Function Minimization

Abstract

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${}^{♮}$-convex function minimization also works for this class of quasi convex functions. The analysis of the exact number of iterations is also extended, revealing the so-called geodesic property of the steepest descent algorithm when applied to semi-strictly quasi L${}^{♮}$-convex functions.

arXiv comment14 pages