منابع مشابه
Minimization of an M-convex Function
We study the minimization of an M-convex function introduced by Murota. It is shown that any vector in the domain can be easily separated from a minimizer of the function. Based on this property, we develop a polynomial time algorithm.
متن کاملScaling Algorithms for M - convex Function Minimization
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 result...
متن کاملM-Convex Function Minimization by Continuous Relaxation Approach: Proximity Theorem and Algorithm
The concept of M-convexity for functions in integer variables, introduced by Murota (1995), plays a primary role in the theory of discrete convex analysis. In this paper, we consider the problem of minimizing an M-convex function, which is a natural generalization of the separable convex resource allocation problem under a submodular constraint and contains some classes of nonseparable convex f...
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 کاملFast 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 ...
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ژورنال
عنوان ژورنال: Discrete Applied Mathematics
سال: 1998
ISSN: 0166-218X
DOI: 10.1016/s0166-218x(97)00140-6