The Experts below are selected from a list of 245361 Experts worldwide ranked by ideXlab platform
C J Umrigar - One of the best experts on this subject based on the ideXlab platform.
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full Optimization of jastrow slater wave functions with application to the first row atoms and homonuclear diatomic molecules
Journal of Chemical Physics, 2008Co-Authors: Julien Toulouse, C J UmrigarAbstract:We pursue the development and application of the recently introduced Linear Optimization method for determining the optimal Linear and nonLinear parameters of Jastrow–Slater wave functions in a variational Monte Carlo framework. In this approach, the optimal parameters are found iteratively by diagonalizing the Hamiltonian matrix in the space spanned by the wave function and its first-order derivatives, making use of a strong zero-variance principle. We extend the method to optimize the exponents of the basis functions, simultaneously with all the other parameters, namely, the Jastrow, configuration state function, and orbital parameters. We show that the Linear Optimization method can be thought of as a so-called augmented Hessian approach, which helps explain the robustness of the method and permits us to extend it to minimize a Linear combination of the energy and the energy variance. We apply the Linear Optimization method to obtain the complete ground-state potential energy curve of the C2 molecule u...
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Full Optimization of Jastrow-Slater wave functions with application to the first-row atoms and homonuclear diatomic molecules
Journal of Chemical Physics, 2008Co-Authors: Julien Toulouse, C J UmrigarAbstract:We pursue the development and application of the recently introduced Linear Optimization method for determining the optimal Linear and nonLinear parameters of Jastrow-Slater wave functions in a variational Monte Carlo framework. In this approach, the optimal parameters are found iteratively by diagonalizing the Hamiltonian matrix in the space spanned by the wave function and its first-order derivatives, making use of a strong zero-variance principle. We extend the method to optimize the exponents of the basis functions, simultaneously with all the other parameters, namely, the Jastrow, configuration state function, and orbital parameters. We show that the Linear Optimization method can be thought of as a so-called augmented Hessian approach, which helps explain the robustness of the method and permits us to extend it to minimize a Linear combination of the energy and the energy variance. We apply the Linear Optimization method to obtain the complete ground-state potential energy curve of the C2 molecule up to the dissociation limit and discuss size consistency and broken spin-symmetry issues in quantum Monte Carlo calculations.We perform calculations for the first-row atoms and homonuclear diatomic molecules with fully optimized Jastrow-Slater wave functions, and we demonstrate that molecular well depths can be obtained with near chemical accuracy quite systematically at the diffusion Monte Carlo level for these systems.
El M Ghami - One of the best experts on this subject based on the ideXlab platform.
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complexity analysis of primal dual interior point methods for Linear Optimization based on a new parametric kernel function with a trigonometric barrier term
Abstract and Applied Analysis, 2014Co-Authors: Guoqiang Wang, El M GhamiAbstract:We introduce a new parametric kernel function, which is a combination of the classic kernel function and a trigonometric barrier term, and present various properties of this new kernel function. A class of large- and small-update primal-dual interior-point methods for Linear Optimization based on this parametric kernel function is proposed. By utilizing the feature of the parametric kernel function, we derive the iteration bounds for large-update methods, , and small-update methods, . These results match the currently best known iteration bounds for large- and small-update methods based on the trigonometric kernel functions.
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interior point methods for Linear Optimization based on a kernel function with a trigonometric barrier term
Journal of Computational and Applied Mathematics, 2012Co-Authors: El M Ghami, Z A Guennoun, S Bouali, Trond SteihaugAbstract:In this paper, we present a new barrier function for primal-dual interior-point methods in Linear Optimization. The proposed kernel function has a trigonometric barrier term. It is shown that in the interior-point methods based on this function for large-update methods, the iteration bound is improved significantly. For small-update interior-point methods, the iteration bound is the best currently known bound for primal-dual interior-point methods.
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a polynomial time algorithm for Linear Optimization based on a new class of kernel functions
Journal of Computational and Applied Mathematics, 2009Co-Authors: El M Ghami, C Roos, I Ivanov, J B M Melissen, Trond SteihaugAbstract:In this paper we present a class of polynomial primal-dual interior-point algorithms for Linear Optimization based on a new class of kernel functions. This class is fairly general and includes the class of finite kernel functions by Y.Q. Bai, M.El Ghami and C. Roos [Y.Q. Bai, M. El Ghami, and C. Roos. A new efficient large-update primal-dual interior-point method based on a finite barrier, SIAM Journal on Optimization, 13 (3) (2003) 766-782]. The proposed functions have a finite value at the boundary of the feasible region. They are not exponentially convex and also not strongly convex like the usual barrier functions. The goal of this paper is to investigate such a class of kernel functions and to show that the interior-point methods based on these functions have favorable complexity results. In order to achieve these complexity results, several new arguments had to be used for the analysis. The iteration bound of large-update interior-point methods based on these functions and analyzed in this paper, is shown to be O(nlognlogn@e). For small-update interior-point methods the iteration bound is O(nlogn@e), which is currently the best-known bound for primal-dual IPMs. We also present some numerical results which show that by using a new kernel function, the best iteration numbers were achieved in most of the test problems.
Christodoulos A Floudas - One of the best experts on this subject based on the ideXlab platform.
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stereochemically consistent reaction mapping and identification of multiple reaction mechanisms through integer Linear Optimization
Journal of Chemical Information and Modeling, 2012Co-Authors: Eric L First, Chrysanthos E Gounaris, Christodoulos A FloudasAbstract:Reaction mappings are of fundamental importance to researchers studying the mechanisms of chemical reactions and analyzing biochemical pathways. We have developed an automated method based on integer Linear Optimization, ILP, to identify optimal reaction mappings that minimize the number of bond changes. An alternate objective function is also proposed that minimizes the number of bond order changes. In contrast to previous approaches, our method produces mappings that respect stereochemistry. We also show how to locate multiple reaction mappings efficiently and determine which of those mappings correspond to distinct reaction mechanisms by automatically detecting molecular symmetries. We demonstrate our techniques through a number of computational studies on the GRI-Mech, KEGG LIGAND, and BioPath databases. The computational studies indicate that 99% of the 8078 reactions tested can be addressed within 1 CPU hour. The proposed framework has been incorporated into the Web tool DREAM (http://selene.princet...
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a comparative theoretical and computational study on robust counterpart Optimization i robust Linear Optimization and robust mixed integer Linear Optimization
Industrial & Engineering Chemistry Research, 2011Co-Authors: Ran Ding, Christodoulos A FloudasAbstract:Robust counterpart Optimization techniques for Linear Optimization and mixed integer Linear Optimization problems are studied in this paper. Different uncertainty sets, including those studied in literature (i.e., interval set; combined interval and ellipsoidal set; combined interval and polyhedral set) and new ones (i.e., adjustable box; pure ellipsoidal; pure polyhedral; combined interval, ellipsoidal, and polyhedral set) are studied in this work and their geometric relationship is discussed. For uncertainty in the left hand side, right hand side, and objective function of the Optimization problems, robust counterpart Optimization formulations induced by those different uncertainty sets are derived. Numerical studies are performed to compare the solutions of the robust counterpart Optimization models and applications in refinery production planning and batch process scheduling problem are presented.
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a hybrid method for peptide identification using integer Linear Optimization local database search and quadrupole time of flight or orbitrap tandem mass spectrometry
Journal of Proteome Research, 2008Co-Authors: Peter A Dimaggio, Christodoulos A Floudas, John R YatesAbstract:A novel hybrid methodology for the automated identification of peptides via de novo integer Linear Optimization, local database search, and tandem mass spectrometry is presented in this article. A ...
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a path selection approach to global pairwise sequence alignment using integer Linear Optimization
Optimization, 2008Co-Authors: Scott R Mcallister, R Rajgaria, Christodoulos A FloudasAbstract:An important and well-studied problem in the area of computational biology is the sequence alignment problem. A novel integer Linear programming (ILP) model has been developed to rigorously address the global pairwise sequence alignment problem. The important components of the model formulation, in addition to its rigour are (a) the natural introduction of functionally important conservation constraints, (b) the creation of a rank-ordered list of the highest scoring alignments and (c) the possible refinement of alignments by pairwise interaction scores. By using a path selection approach that employs some of the algorithmic advantages of dynamic programming methods, this integer Linear Optimization model gains efficiency while maintaining the rigour of the combinatorial Optimization approach. †Dedicated to H. Th. Jongen on the occasion of his 60th birthday.
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analysis and design of metabolic reaction networks via mixed integer Linear Optimization
Aiche Journal, 1996Co-Authors: Vassily Hatzimanikatis, Christodoulos A Floudas, James E BaileyAbstract:Improvements in bioprocess performance can be achieved by genetic modifications of metabolic control structures. A novel Optimization problem helps quantitative understanding and rational metabolic engineering of metabolic reaction pathways. Maximizing the performance of a metabolic reaction pathway is treated as a mixed-integer Linear programming formulation to identify changes in regulatory structure and strength and in cellular content of pertinent enzymes which should be implemented to optimize a particular metabolic process. A regulatory superstructure proposed contains all alternative regulatory structures that can be considered for a given pathway. This approach is followed to find the optimal regulatory structure for maximization of phenylalanine selectivity in the microbial aromatic amino acid synthesis pathway. The solution suggests that from the eight feedback inhibitory loops in the original regulatory structure of this pathway, inactivation of at least three loops and overexpression of three enzymes will increase phenylalanine selectivity by 42%. Moreover, novel regulatory structures with only two loops, none of which exists in the original pathway, could result in a selectivity up to 95%.
Julien Toulouse - One of the best experts on this subject based on the ideXlab platform.
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full Optimization of jastrow slater wave functions with application to the first row atoms and homonuclear diatomic molecules
Journal of Chemical Physics, 2008Co-Authors: Julien Toulouse, C J UmrigarAbstract:We pursue the development and application of the recently introduced Linear Optimization method for determining the optimal Linear and nonLinear parameters of Jastrow–Slater wave functions in a variational Monte Carlo framework. In this approach, the optimal parameters are found iteratively by diagonalizing the Hamiltonian matrix in the space spanned by the wave function and its first-order derivatives, making use of a strong zero-variance principle. We extend the method to optimize the exponents of the basis functions, simultaneously with all the other parameters, namely, the Jastrow, configuration state function, and orbital parameters. We show that the Linear Optimization method can be thought of as a so-called augmented Hessian approach, which helps explain the robustness of the method and permits us to extend it to minimize a Linear combination of the energy and the energy variance. We apply the Linear Optimization method to obtain the complete ground-state potential energy curve of the C2 molecule u...
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Full Optimization of Jastrow-Slater wave functions with application to the first-row atoms and homonuclear diatomic molecules
Journal of Chemical Physics, 2008Co-Authors: Julien Toulouse, C J UmrigarAbstract:We pursue the development and application of the recently introduced Linear Optimization method for determining the optimal Linear and nonLinear parameters of Jastrow-Slater wave functions in a variational Monte Carlo framework. In this approach, the optimal parameters are found iteratively by diagonalizing the Hamiltonian matrix in the space spanned by the wave function and its first-order derivatives, making use of a strong zero-variance principle. We extend the method to optimize the exponents of the basis functions, simultaneously with all the other parameters, namely, the Jastrow, configuration state function, and orbital parameters. We show that the Linear Optimization method can be thought of as a so-called augmented Hessian approach, which helps explain the robustness of the method and permits us to extend it to minimize a Linear combination of the energy and the energy variance. We apply the Linear Optimization method to obtain the complete ground-state potential energy curve of the C2 molecule up to the dissociation limit and discuss size consistency and broken spin-symmetry issues in quantum Monte Carlo calculations.We perform calculations for the first-row atoms and homonuclear diatomic molecules with fully optimized Jastrow-Slater wave functions, and we demonstrate that molecular well depths can be obtained with near chemical accuracy quite systematically at the diffusion Monte Carlo level for these systems.
Guoqiang Wang - One of the best experts on this subject based on the ideXlab platform.
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complexity analysis of primal dual interior point methods for Linear Optimization based on a new parametric kernel function with a trigonometric barrier term
Abstract and Applied Analysis, 2014Co-Authors: Guoqiang Wang, El M GhamiAbstract:We introduce a new parametric kernel function, which is a combination of the classic kernel function and a trigonometric barrier term, and present various properties of this new kernel function. A class of large- and small-update primal-dual interior-point methods for Linear Optimization based on this parametric kernel function is proposed. By utilizing the feature of the parametric kernel function, we derive the iteration bounds for large-update methods, , and small-update methods, . These results match the currently best known iteration bounds for large- and small-update methods based on the trigonometric kernel functions.
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complexity analysis and numerical implementation of primal dual interior point methods for convex quadratic Optimization based on a finite barrier
Numerical Algorithms, 2013Co-Authors: Xinzhong Cai, Guoqiang Wang, Zihou ZhangAbstract:In this paper, we present primal-dual interior-point methods for convex quadratic Optimization based on a finite barrier, which has been investigated earlier for the case of Linear Optimization by Bai et al. (SIAM J Optim 13(3):766---782, 2003). By means of the feature of the finite kernel function, we study the complexity analysis of primal-dual interior-point methods based on the finite barrier and derive the iteration bounds that match the currently best known iteration bounds for large- and small-update methods, namely, $O(\sqrt{n}\log{n}\log{\frac{n}{\varepsilon}})$ and $O(\sqrt{n}\log{\frac{n}{\varepsilon}})$ , respectively, which are as good as the Linear Optimization analogue. Numerical tests demonstrate the behavior of the algorithms with different parameters.
