M-convex functions have various desirable properties as convexity in discrete optimization. We can find a global mininium of an M-convex function by a greedy algorithm, i.e., so-called descent algorithms work for the ...
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M-convex functions have various desirable properties as convexity in discrete optimization. We can find a global mininium of an M-convex function by a greedy algorithm, i.e., so-called descent algorithms work for the minimization. In tills paper;we apply a scaling technique to a greedy algorithm and propose all efficient algorithm for the minimization of all M-convex function. Computational results are also reported.
M-convex functions, introduced by Murota (Adv. Math. 124 (1996) 272;Math. Prog. 83 (1998) 313), enjoy various desirable properties as "discrete convex functions." In this paper, we propose two new polynomial...
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M-convex functions, introduced by Murota (Adv. Math. 124 (1996) 272;Math. Prog. 83 (1998) 313), 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 also specialize our scaling algorithms for the resource allocation problem which is a special case of M-convex function minimization. (C) 2003 Elsevier B.V. All rights reserved.
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 polynomi...
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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. (C) 1998 Elsevier Science B.V. All rights reserved.
The concept of M-convex function, introduced by Murota (1996), isa quantitative generalization of the set of integral points in an integral base polyhedron as well as an extension of valuated matroid of Dress and Wenz...
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The concept of M-convex function, introduced by Murota (1996), isa quantitative generalization of the set of integral points in an integral base polyhedron as well as an extension of valuated matroid of Dress and Wenzel (1990). In this paper, we extend this concept to functions on generalized polymatroids with a view to providing a unified framework for efficiently solvable nonlinear discrete optimization problems.
In this article, we develop a novel framework to study a new class of convex functions known as n-polynomial P-convex functions. The purpose of this article is to establish a new generalization of Ostrowski-type integ...
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In this article, we develop a novel framework to study a new class of convex functions known as n-polynomial P-convex functions. The purpose of this article is to establish a new generalization of Ostrowski-type integral inequalities by using a generalized k-fractional Hilfer-Katugampola derivative. We employ this technique by using the Holder and power-mean integral inequalities. We present analogs of the Ostrowski-type integrals inequalities connected with the n-polynomial P-convex function. Some new exceptional cases from the main results are obtained, and some known results are recaptured. In the end, an application to special means is given as well. The article seeks to create an exciting combination of a convex function and special functions in fractional calculus. It is supposed that this investigation will provide new directions in fractional calculus.
The proximal average operator provides a parametric family of convex functions that continuously transform one convex function into another even when the domains of the two functions do not intersect. We prove that th...
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The proximal average operator provides a parametric family of convex functions that continuously transform one convex function into another even when the domains of the two functions do not intersect. We prove that the proximal average operator is a homotopy with respect to the epi-topology, study its properties, and present several explicit formulas for specific classes of functions. The parametric family inherits desirable properties such as differentiability and strict convexity from the given functions. The results illustrate the powerful tools available in convex and variational analysis from both a theoretical and a computational point of view.
The concept of M-convexity for functions in integer variables, introduced by Murota [Adv. Math., 124 (1996), pp. 272-311], plays a primary role in the theory of discrete convex analysis. In this paper, we consider the...
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The concept of M-convexity for functions in integer variables, introduced by Murota [Adv. Math., 124 (1996), pp. 272-311], 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 function minimization on integer lattice points. We propose a new approach for M-convex function minimization based on continuous relaxation. By establishing proximity theorems we develop a new algorithm based on continuous relaxation. We apply the approach to some special cases of the separable convex quadratic resource allocation problem and the convex quadratic tree resource allocation problem to obtain faster algorithms.
In this note, we show that if a convex function is non-increasing and has a special property we call convex marginal return functions, an effective upper bound can be established using only two function evaluations. F...
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In this note, we show that if a convex function is non-increasing and has a special property we call convex marginal return functions, an effective upper bound can be established using only two function evaluations. Further, we show that this bound can be refined in such a way that the number of function evaluations needed grows linearly with the number of refinements performed.
This article is devoted to smooth approximation of convex functions on Banach spaces with smooth norm. We prove that if X* is a smooth space and f is a w*-lower semicontinuous Lipschitzian convex function on X*, then ...
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This article is devoted to smooth approximation of convex functions on Banach spaces with smooth norm. We prove that if X* is a smooth space and f is a w*-lower semicontinuous Lipschitzian convex function on X*, then there exist two w*-lower semicontinuous, Gateaux differentiable convex function sequences and {g(n)}(n=1)(infinity) such that (1) f(n) < f(n) <= f(n+1) <= f <= g(n+1) <= g(n);(2) f(n)-> f and g(n) -> f uniformly on X*;(3) cl{x* is an element of X* : df(n)(x*) is an element of X} = cl{x* is an element of X* : dg(n)x*) E X} = (C) 2019 Elsevier Inc. All rights reserved.
In this paper we will point out a similar inequality to Hadamard's for h-convex function defined on a disk. Some mappings connected with this inequality and related results are also obtained. (C) 2014 Elsevier Inc...
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In this paper we will point out a similar inequality to Hadamard's for h-convex function defined on a disk. Some mappings connected with this inequality and related results are also obtained. (C) 2014 Elsevier Inc. All rights reserved.
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