David Shalloway [1992]. Application of the Renormalization Group to Deterministic Global Minimization of Molecular Conformation Energy Functions. Global Optimization 2, 281-311.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....on CGU, please visit the CGU home page at: http: cgu.cs.uwec.edu. class includes the DOT [23] algorithm along with a number of other discrete scanning methods [8, 13, 14, 16, 26, 27] The latter encompasses a wider variety of techniques, including molecular dynamics and statistical mechanics [3, 5, 11, 22], Monte Carlo and genetic algorithms [4, 19] underestimation or tunneling methods [6, 7, 21] such as CGU, and procedures for smoothing energy landscapes [15, 17, 20, 25] Instead of utilizing a single refinement technique, we have here coupled a discrete algorithm with a continuous one. While ....

Shalloway., D. (1992), Application of the Renormalization Group to Deterministic Global Minimization of molecular conformation energy functions. J. Global Optim. , 2: 281-311.

....a lowenergy funnel and a bad idea anytime there is a high energy barrier separating low energy basins. To use CGU e#ectively, the domain would need to be separated into parts, each part containing just one distinguished basin. This would combine hierarchical strategies, such as those outlined in [10, 31, 32], with CGU s ability to tunnel to the bottom of bumpy, bowl like landscapes. The original local optimization routine used by CGU was recently replaced with the NPSOL optimization package mentioned earlier. This brand of local optimizer requires fewer function evaluations to converge, which in ....

Shalloway, D. (1992), "Application of the renormalization group to deterministic global minimization of molecular conformation energy functions," Journal of Global Optimization, Vol. 2, 281-311.

....for higher dimensional systems. In any case, just like in the method of bad derivatives, a practical advantage is that the derivative of the effective potential can be calculated directly from the original potential (see equation (14) 32 6. 4 Gaussian packet states (GPS) The work of Shalloway [41] is an attempt to use ideas and methods related to the renormalization group in the field of global optimization. Renormalization group theory tries to find relationships between descriptions of a system at different spatial scales. The potential energy describes the system with infinite ....

.... The equations that determine packet behavior are found by requiring that averages of a smooth function S (x) with a length scale ff (T ) are accurately reproduced with the Gaussian packet states: Z P eq (x 0 )S (x Gamma x 0 ) Z PGP (x 0 )S (x Gamma x 0 ) dx 0 (55) In [41] S (x) is chosen to be a Gaussian. The conditions on the packet parameters are obtained by expanding condition (55) in a Taylor series and equating the first three terms in the series. In [42] the condition is given in slightly different form using the definition of an effective potential that ....

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D. Shalloway, Application of the renormalization group to deterministic global minimization of molecular conformation energy functions, Journal of Global Optimization 2 (1992), 281.

.... applied to problems with hundreds or even thousands of variables in such applications as cluster simulation (Byrd and Schnabel [21, 18, 19, 86, 20] Rosen and Xue [95, 94] Coleman, Shalloway, and Wu [25, 26] protein folding (Byrd and Schnabel [22, 31] Scheraga [62, 74, 73, 54, 55] Shalloway [85, 84, 72], Coleman and Wu [28] and molecular docking (Meza, Plantenga, and Judson [48] Dill, Phillips, and Rosen [35] A global optimization problem requires a local minimizer with the lowest function value among all local optimizers. Certain classes of problems, like convex programming problems, have ....

.... back to the original function, there is a good chance that at least one curve will lead to a global minimizer of the original function (Wu [93] Mor e and Wu [65] The global continuation algorithms have been studied by several research 13 groups including Scheraga et al. [54] Shalloway [85, 84], Coleman, et al. [25] Straub [88, 89] Mor e and Wu [65, 64, 68, 66] and Byrd and Schnabel [86] each having slightly different transforms. In particular, Mor e and Wu [65, 67] developed a class of parallel global continuation algorithms for solving distance geometry problems with application ....

D. Shalloway. Application of the renormalization group to deterministic global minimization of molecular conformation energy functions. J. Global Optim., 2:281--311, 1992. 36

....Transformation Scheme as a General Continuation Approach to Global Optimization with Application to Molecular Conformation Zhijun Wu y Abstract. This paper discusses a generalization of the special function transformation scheme for global energy minimization for molecular conformation used in [3, 4, 14, 15]. Theories for the method as a general continuation approach are established. We show that the method can transform a nonlinear objective function into a class of gradually deformed, but smoother , functions. An optimization procedure can then be applied to the new functions successively, to ....

....most effective use of heuristics specific to protein folding. In response to the challenge of solving the protein folding problem, or the molecular conformation problem in general, many approaches have recently been proposed and studied, either deterministic or undeterministic, such as those in [2, 3, 4, 5, 9, 10, 11, 12, 13, 14, 15, 16, 17]. However, these approaches still can only be applied to small problems, not to the large ones of biological interest. So we believe that developing more efficient and effective algorithms currently is still the most important work to do. The purpose of this work is just to make further progress ....

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David Shalloway [1992]. Application of the Renormalization Group to Deterministic Global Minimization of Molecular Conformation Energy Functions. Global Optimization 2, 281-311.

....modeling. Straub [29] reviews work in this area. The diffusion equation method of Piela, Kostrowicki, and Scheraga [20] is central to our work since the idea of the Gaussian transform underlies the diffusion equation method. Other approaches include the packet annealing method of Shalloway [27, 26] and the effective energy simulated annealing method of Coleman, Shalloway, and Wu [2, 3] We generalize the definition of the Gaussian transform by replacing the Gaussian density function with another density function ae : IR n 7 IR. Definition 2.2 Given a density function ae : IR n 7 IR, ....

D. Shalloway, Application of the renormalization group to deterministic global minimization of molecular conformation energy functions, J. Global Optim., 2 (1992), pp. 281--311.

....However, because of its great practical importance, Problem (1) has been studied intensively in many areas of computational science and optimization. New algorithms on both sequential and parallel machines have been developed; a variety of small to medium sizes of problems have been studied [3, 4, 5, 6, 11, 12, 13, 14, 15, 17, 18, 19, 20]. In recent efforts smoothing techniques are specifically designed for molecular conformation via global minimization. Examples include the diffusion equation method [11, 14] the packet annealing method [17, 18] as well as the effective energy simulated annealing method [4, 5] The basic idea ....

....to medium sizes of problems have been studied [3, 4, 5, 6, 11, 12, 13, 14, 15, 17, 18, 19, 20] In recent efforts smoothing techniques are specifically designed for molecular conformation via global minimization. Examples include the diffusion equation method [11, 14] the packet annealing method [17, 18], as well as the effective energy simulated annealing method [4, 5] The basic idea behind these methods is to use special techniques to smooth a given energy function so that search for a global minimizer becomes more tractable. The methods usually use function transformation schemes to transform ....

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David Shalloway [1992]. Application of the Renormalization Group to Deterministic Global Minimization of Molecular Conformation Energy Functions. Global Optimization 2, 281¸311.

....low function values, where a global minimizer is most likely to be located. Global smoothing was first proposed in the diffusion equation method for protein conformation by Scheraga and coworkers [38, 27, 28, 29, 43] A similar approach was used in the packet annealing algorithm of Shalloway [48, 47] and in the algorithms of Coleman, Shalloway, and Wu [7, 8] for molecular conformation problems. Recent developments of global smoothing and continuation techniques from a mathematical and computational point of view can be found in Wu [51] and Mor e and Wu [35, 34] while Mor e and Wu [36] have ....

D. Shalloway, Application of the renormalization group to deterministic global minimization of molecular conformation energy functions, J. Global Optim., 2 (1992), pp. 281--311.

....the transformed function, tracing their minimizers back to the original function. The idea of transforming a function into a smoother function is appealing; the main approaches include the diffusion equation method of Piela, Kostrowicki, and Scheraga [19] the packet annealing method of Shalloway [24, 23], and the effective energy simulated annealing method of Coleman, Shalloway, and Wu [2, 3] In the diffusion equation method the transformation can be written (see [13, 14] for details) in the form 1 (4 ) n=2 n Z IR n f(y) exp Gamma ky Gamma xk 2 4 dy; 1:4) where is a ....

D. Shalloway, Application of the renormalization group to deterministic global minimization of molecular conformation energy functions, J. Global Optim., 2 (1992), pp. 281--311.

....functions back to the original function. The smoothing transformation was first proposed and studied in the diffusion equation method for protein conformation by Scheraga and coworkers [21, 14, 15, 16, 23] Similar transformations have been used in the packet annealing algorithm of Shalloway [25, 24], and in the algorithms used by Coleman, Shalloway, and Wu [2, 3] for molecular conformation problems. Recent development of this approach from a mathematical and computational point of view can be found in Wu [28] and Mor e and Wu [19] A general review on this approach can also be found in ....

D. Shalloway, Application of the renormalization group to deterministic global minimization of molecular conformation energy functions, J. Global Optim., 2 (1992), pp. 281--311.

....for the force field terms in order to perform the Gaussian integrations. In addition, effective algorithms for identifying bifurcation points in large scale problems must still be developed. The packet annealing method has been tested on met enkephalin after employing a number of simplifications [161]. The effective energy technique has been used in conjunction with simulated annealing [28] and general Gaussian integral transforms have been applied to molecular conformation and distance geometry problems [127] A different approach for deforming the energy surface is to increase the ....

D. Shalloway, Application of the renormalization group to deterministic global minimization of molecular conformation energy functions, J. Global Optim., 2, (1992), 281-311. 30 C. A. FLOUDAS, J. L. KLEPEIS, AND P. M. PARDALOS

....S is the set of all possible structures. In recent years, the molecular conformation problem has been studied extensively in computational sciences, especially in the area of numerical optimization. Many approaches have been investigated, either deterministic or undeterministic, such as those in [3, 4, 11, 12, 15, 16, 18, 19, 22]. However, because of the enormous amount of required computation, most general minimization methods can only be applicable to small problem instances ( 100 atoms) while problems of biological interests tend to be very large ( 1000 atoms) In this paper, we study a general scheme, the build up ....

.... with a class of effective energy functions transformed from the original energy function based on the theory of renormalization groups [13, 23] For the details about the simulated annealing, the effective energy and the effective energy simulated annealing, readers are referred to [1, 10, 22] [18, 19] and [4] Figure 3 contains an outline for the effective energy simulated annealing algorithm, where x is referred to as the current solution, x the perturbed solution, Deltax the random jump, s the random step, l k the maximum number of random trials allowed at step k, A k the step size control ....

David Shalloway [1992]. Application of the Renormalization Group to Deterministic Global Minimization of Molecular Conformation Energy Functions. Global Optimization 2, 281-311.

....many research projects in computational sciences, especially in the area of numerical optimization. A number of approaches exploiting problem specific structures and heuristics have been proposed and studied to find efficient solutions to the problem, either deterministic or undeterministic, e.g. [3, 10, 11, 14, 16, 17, 18, 20, 22]. Most approaches have been applied to small problems, but not to the large problems (typically n = 1000 to 10000) of biological interest. In this paper, we present a global search algorithm which is effective and efficient for finding low energy states of a molecular system. The algorithm ....

....function, and by tracing the change of the global minimum, the algorithm will hopefully reach the global minimum of the original energy function at the end of the annealing. The entire process here is analogous to the homotopy method for local minimization. Similar ideas can also be found in [10, 17, 18]. The effective energy function was first introduced to molecular conformation by Shalloway [17, 18] in the packet annealing algorithm. In this section, we define the central concepts, and show some of its properties with examples. For more mathematical and physical background of this type of ....

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David Shalloway [1992]. Application of the Renormalization Group to Deterministic Global Minimization of Molecular Conformation Energy Functions. Global Optimization 2, 281-311.

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David Shalloway [1992]. Application of the Renormalization Group to Deterministic Global Minimization of Molecular Conformation Energy Functions. Global Optimization 2, 281-311.

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David Shalloway [1992]. Application of the Renormalization Group to Deterministic Global Minimization of Molecular Conformation Energy Functions. Global Optimization 2, 281-311.

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D. Shalloway. Application of the renormalization group to deterministic global minimization of molecular conformation energy function. J. Global Optimization, 2:281--311, 1992.

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