J. J. Mor e. The Levenberg-Marquardt algorithm: Implementation and theory. In Numerical Analysis, Lecture Notes in Mathematics 630, Springer Verlag, 1977.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....generally used for approximately solving the trust region problem based on the standard model, minimize II F(xo) J(xo)d 112 2 (3.1) subject to II d 112 5, where 5o is the current trust region radius. When 5o is shorter than the standard step, the locally constrained optimal method [8] finds a po such that [ d(po) 2 5, where d(po) J(xo)TJ(xo) pI) lj(xo)TF(xo) Then it takes x = xo d(po) The dogleg method is a modification of the trust region algorithm introduced by Powell [10] Rather than finding a point x = xo d(po) on the curve d(po) such that [ x xo [ ....

J. J. Mor, The Levenberg-Marquardt Algorithm: Implementation and Theory, in Numerical Analysis, G. A. Watson, ed., Lecture Notes in Mathematics, vol. 630, Springer-Verlag, Berlin, 1977, pp. 105-116.

....by minimizing an objective function J = N i=1 #u u# , 7) where #. # denotes the Euclidean norm, N is the number of points, u are coordinates of points measured in the image, and u are their coordinates reprojected by the camera model. A MATLAB implementation of the Levenberg Marquardt [6] minimization was employed in order to minimize the objective function (7) The rotational matrix R has three degrees of freedom, as well as the vector of translation T, see (2) The image center, scale ratio of the image axes #, and the four parameters of the mapping between the light rays and ....

J.J. Mor e. The levenberg-marquardt algorithm: Implementation and theory. In G. A. Watson, editor, Numerical Analysis, Lecture Notes in Mathematics 630, pages 105--116. Springer Verlag, 1977.

....de Inform tica, Universidad Jaime I, Campus Penyeta Roja, 12071 Castell6n, Spain, gquintan inf. uj i. es. Same address as first author; quintana inf. uji. es. Department of Computer Science, University of Tennessee at Knoxville, Tennessee, USA, pet it or cs. art. edu. least squares problems [31], solution of integral equations [18] and calculation of splines [22] Specifically, the LLS problem consists in finding the vector x that satisfies ruin[lAx b[12 (1) where A is an m x n coefficient matrix and b is a vector of n components. Basically, depending on the properties of A, the ....

J. MoR, The Levenberg-Marquardt algorithm: Implementation and the- ory, in Proceedings of the Dundee Conference on Numerical Analysis, G. A. Watson, ed., Berlin, 1978, Springer-Verlag.

....the following (existing) Minimal Residual AIN schemes: ffl linesearch, the backtracking linesearch technique [4, pp. 458] ffl dogleg, the model trust region approach as proposed in [4, pp. 462] ffl nngcg, a variant of the method proposed in [2] solving (8) by the LevenbergMarquardt algorithm [20]; ffl gnks, the method proposed in [15] and the (new) Restricted Minimal Residual AIN schemes: ffl rmr a, choosing W k = V k ; and ffl rmr b, choosing W k = W k Gamma1 ; w k ] where w k is the component of J k p k orthogonal to W k Gamma1 . For these last two schemes, the minimization ....

J. J. Mor' e, The Levenberg-Marquardt algorithm: Implementation and theory, in Numerical Analysis, G. A. Watson, ed., vol. 630 of Lecture Notes in Mathematics, Springer-Verlag, Berlin, Heidelberg, New York, 1977, ch. 105-116.

....problems, one corresponding to each of the three cost functions of eqs. 13) 16) 18) The following remarks can be made regarding each problem. Constant coefficients. We need to estimate four coefficients: A, do, dl, d2. The method used for minimization is the Levenberg Marquardt algorithm [16]. Neural coefficients. The topology of the ANN s used is 1 2 1 (i.e. one input unit, two hidden units and one output units) The hidden units have sigmoid transfer function and the output unit has linear transfer function. The total number of weights is then 12; including the ;0 variable, we have ....

J.J. Mor5 (1995). The Levenberg-Marquardt Algorithm: Implementation and Theory, in: G.A.Watson (ed.), Numerical Analysis, Lecture Notes in Mathematics, vol. 630, pp. 105- 116.Heidelberg: Springer Verlag.

....very unstable. We chose a Levenberg Marquardt type algorithm we used in the past for the resolution of an inverse problem where stability was quite difficult to manage. We obtained good results with it and it seems to be a quite robust algorithm. We can find a description of this algorithm in [7]. Or course, if we test this algorithm with dissimilarities corresponding to exact distances, we obtain the exact point distribution: we can do it easily with more simple algorithms. But if dissimilarities are not exact distances: approximated distances (with errors in the measurements for ....

Mor'e J.J.: 1977, 'The Levenberg-Marquardt Algorithm: Implementation and Theory' Numerical Analysis, Lecture Notes in Mathematics, SpringerVerlag, Vol. 630 pp. 105--116

....algorithms that we have designed to date for the AATC system have targeted off nominal conditions, such as backups, braking due to interference, and low train motor voltages due to excessive power demand. We 4 SIAG OPT Views and News will discuss only two examples here, but more are contained in [2] and [3] The first control algorithm relates to backup recovery. A backup occurs if a train stops for a period that is several times the scheduled headway. This can occur in either a station or between stations. An algorithm was developed to recognize backups and to reduce the speeds of ....

....license to publish or reproduce the published form of this contribution, or allow others to do so, for United States Government purposes. REFERENCES [1] E. Nishinaga, J.A. Evans, and G.L. Mayhew. Wireless Advanced Automatic Train Control. IEEE Vehicular Technology News, 41 (p. 13) 1994. [2] S.P. Gordon and D.G. Lehrer. Coordinated Train Control and Energy Management Control Strategies. 1998 ASME IEEE Joint Railroad Conference (IEEE, 1998) pp.165 176. 3] S.P. Gordon and D.G. Lehrer. Service and EnergyRelated Optimization of AATC. 1998 Rapid Transit Conference (APTA, 1998) ....

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Jorge J. Mor'e. The Levenberg-Marquardt algorithm: Implementation and theory. In G.A. Watson, editor, Lecture Notes in Mathematics, No. 630--Numerical Analysis, pages 105--116. Springer-Verlag, 1978.

....v 1 the start and end values, L s the segment length, t the time and n the curve form coefficient, which is found by minimizing the least square error for the segment, Error = env ( t ) env0 ( t ) 2 . 7) The curve fitting problem is nonlinear, and the LevenbergMarquardt method [8] is used to solve it. The initial values for the curve fit are found in the log domain of equation (6) using LMS [9] 5. ENVELOPE RECONSTRUCTION The envelope can now be recreated, using the start, attack, sustain, release and end split point times, amplitudes and curve forms and concatenating ....

J. J. Mor, "The Levenberg-Marquardt algorithm: Implementation and theory". Lecture notes in mathematics, Edited by G. A. Watson, Springer-Verlag, 1977.

.... solution of the unconstrained regularized linear least squares problem minfkDG(x k )s G(x k )k 2 ksk 2 : s 2 R n g (16) and 0 is determined from the scalar equation fi( ks( k Gamma Delta k = 0: 17) An appropriate algorithm for solving (16) and (17) was described by Mor e [14], which has become part of most trust region codes. Since fi( is nonlinear in , 17) has to be solved iteratively, too, so that the solution s( of (16) has to be repeatedly evaluated for different values of , as reported by Mor e [14] and confirmed by Gay [9] Let us now consider a common ....

....algorithm for solving (16) and (17) was described by Mor e [14] which has become part of most trust region codes. Since fi( is nonlinear in , 17) has to be solved iteratively, too, so that the solution s( of (16) has to be repeatedly evaluated for different values of , as reported by Mor e [14] and confirmed by Gay [9] Let us now consider a common function F (x; F : D x Theta D ae R n Theta R 1 R m ; m n (18) and define f(x; 1 2 kF (x; k 2 where f is bounded below and then minff(x; 0) x 2 R n g (19) has to be determined. For a given (x o ; o ) ....

J.J. Mor'e. The Levenberg--Marquardt algorithm: Implementation and theory, in Lecture Notes in Mathematics 630 (G.A. Watson, ed.) New York: Springer-Verlag, 1978.

....standard Cholesky. It is interesting to remark that these methods are related to l 2 trust region Levenberg Marquardt algorithms, although the latter are using a rank n update rather than the normally considerably lower rank updates used above, Hebden, 1973, Levenberg, 1944, Marquardt, 1963 and Mor e, 1978). The iterative method of choice is that of (preconditioned) conjugate gradients. Thus we need to solve (2.8) where B is a (possibly perturbed) approximation to the Hessian matrix r xx f . The perturbation may be obtained as the conjugate gradient algorithm proceeds in what we think is an ....

J. J. Mor'e. The Levenberg-Marquardt algorithm: implementation and theory. In G. A. Watson, editor, Proceedings Dundee 1977. Springer Verlag, Berlin, 1978. Lecture Notes in Mathematics.

....with the real vehicle properties. For the solution of (3) 4) several gradient based optimization methods as well as an evolutionary algorithm have been investigated [2] In the sequel, we present results obtained from the Gauss Newton method NLSCON [8] the Levenberg Marquardt algorithm LMDER [7], the sequential quadratic programming method NLSSOL [5] and the implicit ltering code IFFCO [6] which is designed for solving noisy minimization problems. 4 Parallel Optimization For the solution of the parameter estimation problem a program frame was implemented which integrates veDYNA in ....

More, J.J.: The Levenberg-Marquardt algorithm: implementation and theory. In: Dold, A., Eckmann, B. (eds.): Numerical Analysis. Lecture Notes in Mathematics, Vol. 630. Springer-Verlag, Berlin Heidelberg (1978) 105-116

....used and their distances to the reference frame, the sizes of the blocks and what they represent in terms of image information and the residual value of the objective function for each block. The optimization method used is based on the Levenberg Marquardt trust region method as given by Mor e[18]. In the case where the approximation of the Hessian is close to singularity, the algorithm is modified as given by Gay[19] The outcome is better convergence properties in all cases including those when the Hessian is singular. This of course is at the expense of added computational complexity. ....

....METHOD 38 Computing the step s A model trust region strategy is used to compute the step Deltad k . We need to find a region or neighborhood N where the quadratic approximation (4.2) truly models the objective function. The discussion in this section is based on work by Gay [19] and Mor e [18]. The two dimensional neighborhood N has the form N = fy 2 R 2 : kDyk ffig (4.8) where D is a scaling matrix and ffi is the trust radius. An Optimal Locally Constrained (OLC) step s is defined by theorem 2.1 in [19] Theorem: If U(d) and N are given by (4.2) and (4.8) respectively with ffi ....

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Mor'e J., The Levenberg-Marquardt Algorithm: Implementation and Theory, Lecture Notes in Mathematics No. 630 Numerical Analysis, G. Watson, Ed., SprongerVerlag, New York, 197, pp. 105-116.

.... unconstrained and bound constrained optimization, using sparse factorizations, have been proposed by Gill et al. 1992) Conn et al. 1991) and Schlick (1992) We should also mention the philosophically different but mechanically similar class of 2 trust region methods (see, e.g. Hebden, 1973, Mor e, 1978, Sorensen, 1980 and Gay, 1981) Here perturbations of the form E (k) k) I may be made to H(x (k) for some appropriate scalar (k) in order to make B (k) positive semi definite. We note the difference of approach between these methods and the modified Cholesky methods, in that ....

J. J. Mor'e. The Levenberg-Marquardt algorithm: implementation and theory. In G. A. Watson, editor, Proceedings Dundee 1977, Berlin, 1978. Springer Verlag. Lecture Notes in Mathematics.

....computational costs involved in the QR factorization 1 Plassmann [P90] considers the large sparse case. 2 For a more detailed description of the Levenberg Marquardt algorithm, including step acceptance and convergence criteria, we refer the interested reader to the excellent article by Mor e [M78]. 2 stage often dominate the Jacobian approximation stage. Thus, we have chosen to pursue a roworiented QR factorization algorithm 3 . We would like to take advantage of this data distribution in approximating the Jacobian whenever possible. Let I i , i = 1; p, be a partition of the ....

....that there exist effective algorithms to perform this reduction. However, efficient solution of triangular systems is also important in this context. In fact, for each iteration involving a solution of (1. 4) there are two associated triangular solutions that are used to bracket the solution [M78]. Recently, much work has been done on the parallel solution of triangular systems [C86, LC88, LC89, HR88] We used the triangular solution algorithms developed by Li and Coleman in our implementations, but it should be noted that the efficiencies of these algorithms are not nearly as good as ....

J. J. Mor'e, The Levenberg-Marquardt algorithm: implementation and theory, in Lecture Notes in Mathematics, No. 630-Numerical Analysis, G. Watson, ed., Springer-Verlag, New York, 1978, pp. 105-116.

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J. J. Mor e. The Levenberg-Marquardt algorithm: Implementation and theory. In Numerical Analysis, Lecture Notes in Mathematics 630, Springer Verlag, 1977.

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J. Mor' e, The Levenberg-Marquardt algorithm: Implementation and theory, in Proceedings of the Dundee Conference on Numerical Analysis, G. A. Watson, ed., Berlin, 1978, Springer-Verlag.

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Mor, J. J. The Levenberg-Marquardt algorithm: Implementation and theory. Lecture notes in mathematics, Edited by G. A. Watson, SpringerVerlag, 1977.

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Mor, J. J. The Levenberg-Marquardt algorithm: Implementation and theory. Lecture notes in mathematics, Edited by G. A. Watson, Springer-Verlag, 1977.

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J. J. Mor, "The Levenberg-Marquardt algorithm, implementation and theory," in Numerical Analysis, G. A. Watson, Editor, Lecture Notes in mathematics 630, Springer-Verlag, 1977.

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J. J. Mor, "The Levenberg-Marquardt algorithm: Implementation and theory". Lecture notes in mathematics, Edited by G. A. Watson, Springer-Verlag, 1977.

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J.J. MOR, The Levenberg-Marquardt algorithm: implementation and theory, in Numerical Analysis: Proceedings of the biennial conference, Dundee 1977.

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J. J. Mor e, The Levenberg-Marquardt algorithm: implementation and theory, in Numerical Analysis: Proceedings of the biennial conference, Dundee

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J. J. More, The Levenberg-Marquardt algorithm: Implementation and theory, Numerical Analysis. Proceedings, Dundee 1977.

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J.J. Mor, The Levenberg-Marquardt algorithm: Implementation and theory. in G.A. Watson, ed., Lecture Notes in Mathematics 630, Springer-Verlag, Berlin, Heidelberg and New York, 1977, pp. 105-119.

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J.J. Mor'e, "The Levenberg-Marquardt algorithm: implementation and theory", in: G.A. Watson, ed., Proc. Dundee Conference on Numerical Analysis (SpringerVerlag, Berlin, 1978)

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