We design new projective forward-backward algorithms for constrained minimization problems. We then discuss its weak convergence via a new linesearch that the hypothesis on the Lipschitz constant of the gradient of fu...
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We design new projective forward-backward algorithms for constrained minimization problems. We then discuss its weak convergence via a new linesearch that the hypothesis on the Lipschitz constant of the gradient of functions is avoided. We provide its applications to solve image deblurring and image inpainting. Finally, we discuss the optimal selection of parameters that are proposed in algorithms in terms of PSNR and SSIM. It reveals that our new algorithm outperforms some recent methods introduced in the literature.
In this study, we consider the following minimization problem on a bounded smooth domain Omega in R-N: S' : = inf {parallel to del u parallel to(2)(2) /parallel to u parallel to(2)(2)* vertical bar u is an element...
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In this study, we consider the following minimization problem on a bounded smooth domain Omega in R-N: S' : = inf {parallel to del u parallel to(2)(2) /parallel to u parallel to(2)(2)* vertical bar u is an element of H-1 (Omega) \ minimization problem, integral(Omega) vertical bar u vertical bar(2)*(-2)u = 0}. This minimization problem plays a crucial role in the study of L-p-Lyapunov type inequalities (1 <= p <= infinity) for linear partial differential equations with Neumann boundary conditions. In this study, we prove the existence of minimizers of S'. As a consequence, we prove the L-p-Lyapunov type inequality in the critical case, which was left open in [4]. (C) 2015 Elsevier Inc. All rights reserved.
We study minimization problems on Hardy-Sobolev type inequality. We consider the case where singularity is in interior of bounded domain Omega subset of R-N. The attainability of best constants for Hardy-Sobolev type ...
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We study minimization problems on Hardy-Sobolev type inequality. We consider the case where singularity is in interior of bounded domain Omega subset of R-N. The attainability of best constants for Hardy-Sobolev type inequalities with boundary singularities have been studied so far, for example Ghoussoub and Kang (Ann Inst Henri Poincare Anal Non Lineaire 21(6):767-793, 2004), Ghoussoub and Robert (IMRP 21867:1-85, 2006), Ghoussoub and Robert (Trans Am Math Soc 361(9):4843-4870, 2009) etc.... According to their results, the mean curvature of partial derivative Omega at singularity affects the attainability of the best constants. In contrast with boundary singularity case, in interior singularity case it is well known that the best Hardy-Sobolev constant mu(s)(Omega) := {integral(Omega)vertical bar del u|(2) dx vertical bar u is an element of H-0(1) (Omega), integral(Omega) |u|(2*(s))/|x|(s) dx = 1} is never achieved for all bounded domain Omega. We can see that the position of singularity on domain is related to the existence of minimizer. In this paper, we consider the attainability of the best constant for the embedding H-1 (Omega) hooked right arrow L-2*(s)(Omega, |x|(-s) dx) for bounded domain Omega with 0 is an element of Omega. In this problem, scaling invariance doesn't hold and we can not obtain information of singularity like mean curvature.
In this paper, we introduce a modified Halpern algorithm for approximating a common solution of split equality convex minimization problem and split-equality fixed-point problem for Bregman quasi-nonexpansive mappings...
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In this paper, we introduce a modified Halpern algorithm for approximating a common solution of split equality convex minimization problem and split-equality fixed-point problem for Bregman quasi-nonexpansive mappings in p-uniformly convex and uniformly smooth Banach spaces. We introduce a generalized step size such that the algorithm does not require a prior knowledge of the operator norms and prove a strong convergence theorem for the sequence generated by our algorithm. We give some applications and numerical examples to show the consistency and accuracy of our algorithm. Our results complement and extend many other recent results in this direction in literature.
The branch and bound method has been offered and realized for a minimization problem of the weighted length of a connecting grid at linear placing of rectangular elements. The rule of branching of admissible set on su...
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The branch and bound method has been offered and realized for a minimization problem of the weighted length of a connecting grid at linear placing of rectangular elements. The rule of branching of admissible set on subsets has been considered. The estimation of an admissible set has been offered and proved. The illustrative example has been given.
Let H be a Hilbert space. Consider on H a sequence of nonexpansive mappings {T(n)} with common fixed points, an equilibrium function G, a contraction f with coefficient 0< alpha < 1 and a strongly positive linea...
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Let H be a Hilbert space. Consider on H a sequence of nonexpansive mappings {T(n)} with common fixed points, an equilibrium function G, a contraction f with coefficient 0< alpha < 1 and a strongly positive linear bounded operator A with coefficient (gamma) over bar 0. Let 0 < gamma < (gamma) over bar/alpha We define a suitable Mann type algorithm which strongly converges to the unique solution of the minimization problem(x is an element of C) 1/2 (Ax,x) - h (x), where h is a potential function for f and C is the intersection of the equilibrium points and the common fixed points of the sequence {T(n)}. (C) 2010 Elsevier Ltd. All rights reserved.
In this paper, we consider the following minimization problem:where , , , and are given. An efficient inequality relaxation technique is presented to relax the matrix inequality constraint so that there is an optimal ...
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In this paper, we consider the following minimization problem:where , , , and are given. An efficient inequality relaxation technique is presented to relax the matrix inequality constraint so that there is an optimal solution which is (R,S)-symmetric that minimize , and also satisfies the corrected matrix inequality constraint. A hybrid algorithm with convergence analysis is given to solve this problem. Numerical examples show that the algorithm requires less CPU times when compared with some other methods.
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