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Audrey Repetti - One of the best experts on this subject based on the ideXlab platform.
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Variable Metric Forward---Backward Algorithm for Minimizing the Sum of a Differentiable Function and a Convex Function
Journal of Optimization Theory and Applications, 2013Co-Authors: Emilie Chouzenoux, Jean-christophe Pesquet, Audrey RepettiAbstract:We consider the minimization of a Function G defined on ${ \mathbb{R} } ^{N}$ , which is the sum of a (not necessarily Convex) differentiable Function and a (not necessarily differentiable) Convex Function. Moreover, we assume that G satisfies the Kurdyka---?ojasiewicz property. Such a problem can be solved with the Forward---Backward algorithm. However, the latter algorithm may suffer from slow convergence. We propose an acceleration strategy based on the use of variable metrics and of the Majorize---Minimize principle. We give conditions under which the sequence generated by the resulting Variable Metric Forward---Backward algorithm converges to a critical point of G. Numerical results illustrate the performance of the proposed algorithm in an image reconstruction application.
Maslina Darus - One of the best experts on this subject based on the ideXlab platform.
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the hadamard s inequality for s Convex Function
2008Co-Authors: Mohammad W Alomari, Maslina DarusAbstract:A monotone nondecreasing mapping connected with Hadamard– type inequality for s–Convex Function and some applications are given.
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co ordinated s Convex Function in the first sense with some hadamard type inequalities
2008Co-Authors: Mohammad W Alomari, Maslina DarusAbstract:In this paper a Hadamard’s type inequality of s–Convex Function in first sense and s–Convex Function of 2–variables on the co–ordinates are given. A monotonic nondecreasing mapping connected with the Hadamard’s inequality for Lipschitzian s–Convex mapping in the first sense of one variable is established.
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the hadamard s inequality for s Convex Function of 2 variables on the co ordinates
2008Co-Authors: Mohammad W Alomari, Maslina DarusAbstract:In this paper the extension of Hadamard’s type inequality for s– Convex Function and s–Convex Functions on the co-ordinates defined in 2-variables and some applications are given.
Akiyoshi Shioura - One of the best experts on this subject based on the ideXlab platform.
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m Convex Function minimization by continuous relaxation approach proximity theorem and algorithm
Siam Journal on Optimization, 2011Co-Authors: Satoko Moriguchi, Akiyoshi Shioura, Nobuyuki TsuchimuraAbstract: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.
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MATHEMATICAL ENGINEERING TECHNICAL REPORTS Note on L ♮ -Convex Function Minimization Algorithms: Comparison of Murota's and Kolmogorov's Algorithms
2006Co-Authors: Akiyoshi ShiouraAbstract:The concept of L-Convexity is introduced by Fujishige–Murota (2000) as a discrete Convexity for Functions defined over the integer lattice. The main aim of this note is to understand the difference of the two algorithms for L-Convex Function minimization: Murota’s steepest descent algorithm (2003) and Kolmogorov’s primal algorithm (2005).
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fast scaling algorithms for m Convex Function minimization with application to the resource allocation problem
Discrete Applied Mathematics, 2004Co-Authors: Akiyoshi ShiouraAbstract: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.
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m Convex Function on generalized polymatroid
Mathematics of Operations Research, 1999Co-Authors: Kazuo Murota, Akiyoshi ShiouraAbstract:The concept of M-Convex Function, introduced by Murota 1996, is a 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.
Jinrong Wang - One of the best experts on this subject based on the ideXlab platform.
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New Riemann-Liouville fractional Hermite-Hadamard inequalities via two kinds of Convex Functions
Journal of Interdisciplinary Mathematics, 2017Co-Authors: Zeng Lin, Jinrong WangAbstract:AbstractIn this paper, we establish another important integral identity for once differentiable Function involving Riemann-Liouville fractional integrals, which will be used to derive some new Riemann-Liouville fractional Hermite-Hadamard inequalities via r-Convex Function and geometric-arithmetically s-Convex Function respectively.
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Applying GG-Convex Function to Hermite-Hadamard Inequalities Involving Hadamard Fractional Integrals
International Journal of Mathematics and Mathematical Sciences, 2014Co-Authors: Zhi Zhang, Jinrong Wang, Jianhua DengAbstract:By virtue of fractional integral identities, incomplete beta Function, useful series, and inequalities, we apply the concept of GG-Convex Function to derive new type Hermite-Hadamard inequalities involving Hadamard fractional integrals. Finally, some applications to special means of real numbers are demonstrated.
Jean-philippe Chancelier - One of the best experts on this subject based on the ideXlab platform.
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Auxiliary problem principle and inexact variable metric forward-backward algorithm for minimizing the sum of a differentiable Function and a Convex Function
arXiv: Optimization and Control, 2015Co-Authors: Jean-philippe ChancelierAbstract:In view of the minimization of a Function which is the sum of a differentiable Function $f$ and a Convex Function $g$ we introduce descent methods which can be viewed as produced by inexact auxiliary problem principle or inexact variable metric forward-backward algorithm. Assuming that the global objective Function satisfies the Kurdyka-Lojasiewicz inequality we prove the convergence of the proposed algorithm weakening assumptions found in previous works.