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Convergence Properties of the NelderMead Simplex Method in Low Dimensions
 SIAM Journal of Optimization
, 1998
"... Abstract. The Nelder–Mead simplex algorithm, first published in 1965, is an enormously popular direct search method for multidimensional unconstrained minimization. Despite its widespread use, essentially no theoretical results have been proved explicitly for the Nelder–Mead algorithm. This paper pr ..."
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Cited by 598 (3 self)
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in two dimensions and a set of initial conditions for which the Nelder–Mead algorithm converges to a nonminimizer. It is not yet known whether the Nelder–Mead method can be proved to converge to a minimizer for a more specialized class of convex functions in two dimensions. Key words. direct search
An iterative method for the solution of the eigenvalue problem of linear differential and integral
, 1950
"... The present investigation designs a systematic method for finding the latent roots and the principal axes of a matrix, without reducing the order of the matrix. It is characterized by a wide field of applicability and great accuracy, since the accumulation of rounding errors is avoided, through the ..."
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Cited by 537 (0 self)
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the process of "minimized iterations". Moreover, the method leads to a well convergent successive approximation procedure by which the solution of integral equations of the Fredholm type and the solution of the eigenvalue problem of linear differential and integral operators may be accomplished. I.
Active Contours without Edges
, 2001
"... In this paper, we propose a new model for active contours to detect objects in a given image, based on techniques of curve evolution, MumfordShah functional for segmentation and level sets. Our model can detect objects whose boundaries are not necessarily defined by gradient. We minimize an energy ..."
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Cited by 1206 (38 self)
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In this paper, we propose a new model for active contours to detect objects in a given image, based on techniques of curve evolution, MumfordShah functional for segmentation and level sets. Our model can detect objects whose boundaries are not necessarily defined by gradient. We minimize
SIGNAL RECOVERY BY PROXIMAL FORWARDBACKWARD SPLITTING
 MULTISCALE MODEL. SIMUL. TO APPEAR
"... We show that various inverse problems in signal recovery can be formulated as the generic problem of minimizing the sum of two convex functions with certain regularity properties. This formulation makes it possible to derive existence, uniqueness, characterization, and stability results in a unifi ..."
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Cited by 509 (24 self)
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unified and standardized fashion for a large class of apparently disparate problems. Recent results on monotone operator splitting methods are applied to establish the convergence of a forwardbackward algorithm to solve the generic problem. In turn, we recover, extend, and provide a simplified analysis
Nonlinear total variation based noise removal algorithms
, 1992
"... A constrained optimization type of numerical algorithm for removing noise from images is presented. The total variation of the image is minimized subject to constraints involving the statistics of the noise. The constraints are imposed using Lagrange multipliers. The solution is obtained using the g ..."
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Cited by 2271 (51 self)
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the gradientprojection method. This amounts to solving a time dependent partial differential equation on a manifold determined by the constraints. As t ~ 0o the solution converges to a steady state which is the denoised image. The numerical algorithm is simple and relatively fast. The results appear
KSVD: An Algorithm for Designing Overcomplete Dictionaries for Sparse Representation
, 2006
"... In recent years there has been a growing interest in the study of sparse representation of signals. Using an overcomplete dictionary that contains prototype signalatoms, signals are described by sparse linear combinations of these atoms. Applications that use sparse representation are many and inc ..."
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Cited by 935 (41 self)
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signal representations. Given a set of training signals, we seek the dictionary that leads to the best representation for each member in this set, under strict sparsity constraints. We present a new method—the KSVD algorithm—generalizing the umeans clustering process. KSVD is an iterative method
On active contour models and balloons
 CVGIP: Image
"... The use.of energyminimizing curves, known as “snakes, ” to extract features of interest in images has been introduced by Kass, Witkhr & Terzopoulos (Znt. J. Comput. Vision 1, 1987,321331). We present a model of deformation which solves some of the problems encountered with the original method. ..."
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Cited by 588 (43 self)
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The use.of energyminimizing curves, known as “snakes, ” to extract features of interest in images has been introduced by Kass, Witkhr & Terzopoulos (Znt. J. Comput. Vision 1, 1987,321331). We present a model of deformation which solves some of the problems encountered with the original method
Differential Evolution  A simple and efficient adaptive scheme for global optimization over continuous spaces
, 1995
"... A new heuristic approach for minimizing possibly nonlinear and non differentiable continuous space functions is presented. By means of an extensive testbed, which includes the De Jong functions, it will be demonstrated that the new method converges faster and with more certainty than Adaptive Simula ..."
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Cited by 427 (5 self)
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A new heuristic approach for minimizing possibly nonlinear and non differentiable continuous space functions is presented. By means of an extensive testbed, which includes the De Jong functions, it will be demonstrated that the new method converges faster and with more certainty than Adaptive
Efficient Implementation of Weighted ENO Schemes
, 1995
"... In this paper, we further analyze, test, modify and improve the high order WENO (weighted essentially nonoscillatory) finite difference schemes of Liu, Osher and Chan [9]. It was shown by Liu et al. that WENO schemes constructed from the r th order (in L¹ norm) ENO schemes are (r +1) th order accur ..."
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Cited by 412 (38 self)
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waves. We also prove that, for conservation laws with smooth solutions, all WENO schemes are convergent. Many numerical tests, including the 1D steady state nozzle flow problem and 2D shock entropy waveinteraction problem, are presented to demonstrate the remarkable capability of the WENO schemes
Convergence of a block coordinate descent method for nondifferentiable minimization
 J. OPTIM THEORY APPL
, 2001
"... We study the convergence properties of a (block) coordinate descent method applied to minimize a nondifferentiable (nonconvex) function f(x1,...,xN) with certain separability and regularity properties. Assuming that f is continuous on a compact level set, the subsequence convergence of the iterate ..."
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Cited by 298 (3 self)
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We study the convergence properties of a (block) coordinate descent method applied to minimize a nondifferentiable (nonconvex) function f(x1,...,xN) with certain separability and regularity properties. Assuming that f is continuous on a compact level set, the subsequence convergence
Results 1  10
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4,619