Scaling Algorithms for M - convex Function Minimization
نویسندگان
چکیده
M-convex functions have various desirable properties as convexity in discrete optimization. We can find a global minimum of an M-convex function by a greedy algorithm, i.e., so-called descent algorithms work for the minimization. In this paper, we apply a scaling technique to a greedy algorithm and propose an efficient algorithm for the minimization of an M-convex function. Computational results are also reported.
منابع مشابه
Fast scaling algorithms for M-convex function minimization with application to the resource allocation problem
M-convex functions, introduced by Murota (1996, 1998), enjoy various desirable properties as “discrete convex functions.” In this paper, we propose two new polynomial-time scaling algorithms for the minimization of an M-convex function. Both algorithms apply a scaling technique to a greedy algorithm for M-convex function minimization, and run as fast as the previous minimization algorithms. We ...
متن کاملOn Steepest Descent Algorithms for Discrete Convex Functions
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. Combination of the present results with a standard scaling approach leads to an efficient algor...
متن کاملMATHEMATICAL ENGINEERING TECHNICAL REPORTS Discrete L-/M-Convex Function Minimization Based on Continuous Relaxation
We consider the problem of minimizing a nonlinear discrete function with L-/M-convexity proposed in the theory of discrete convex analysis. For this problem, steepest descent algorithms and steepest descent scaling algorithms are known. In this paper, we use continuous relaxation approach which minimizes the continuous variable version first in order to find a good initial solution of a steepes...
متن کاملSubmodular Function Minimization and Maximization in Discrete Convex Analysis
This paper sheds a new light on submodular function minimization and maximization from the viewpoint of discrete convex analysis. L-convex functions and M-concave functions constitute subclasses of submodular functions on an integer interval. Whereas L-convex functions can be minimized efficiently on the basis of submodular (set) function minimization algorithms, M-concave functions are identif...
متن کاملScaling and Proximity Properties of Integrally Convex Functions
In discrete convex analysis, the scaling and proximity properties for the class of L-convex functions were established more than a decade ago and have been used to design efficient minimization algorithms. For the larger class of integrally convex functions of n variables, we show here that the scaling property only holds when n ≤ 2, while a proximity theorem can be established for any n, but o...
متن کامل