Steepest Descent Algorithm for M-convex Function Minimization Using Long Step Length

Abstract

We consider the minimization of an M-convex function, which is a discrete convexity concept for functions on the integer lattice points. It is known that a minimizer of an Mconvex function can be obtained by the steepest descent algorithm. In this paper, we propose an effective use of long step length in the steepest descent algorithm, aiming at the reduction in the running time. In particular, we obtain an improved time bound by using long step length. We also consider the constrained M-convex function minimization and show that long step length can be applied to a variant of steepest descent algorithm as well.