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  • 1
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 115 (2001), S. 4463-4472 
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: Highly accurate relativistic Gaussian basis sets are developed for the 103 elements from H(Z=1) to Lr (Z=103). Orbital exponents are optimized by minimizing the atomic self-consistent field (SCF) energy with the scalar relativistic third-order Douglas–Kroll approximation. The basis sets are designed to have equal quality and to be appropriate for the incorporation of relativistic effects. The basis set performance is tested by calculations on prototypical molecules, hydrides, and dimers of copper, silver, and gold using SCF, Møller–Plesset theory, and the singles and doubles coupled-cluster methods with and without perturbative triples [CCSD, CCSD(T)]. Spectroscopic constants and dissociation energies are reported for the ground state of each species. The effects of relativity, electron correlation, and the basis set superposition error (BSSE) are investigated. At the BSSE corrected CCSD(T) level, the mean absolute error relative to experiment in De for three dimers (hydrides) is 0.13 (0.09) eV; for Re the error is 0.024 (0.003) Å, and for ωe it is 2 (13) cm−1. These illustrative calculations confirm that the present basis sets fulfill their design objectives. © 2001 American Institute of Physics.
    Type of Medium: Electronic Resource
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  • 2
    Electronic Resource
    Electronic Resource
    s.l. : American Chemical Society
    The @journal of organic chemistry 42 (1977), S. 1856-1862 
    ISSN: 1520-6904
    Source: ACS Legacy Archives
    Topics: Chemistry and Pharmacology
    Type of Medium: Electronic Resource
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  • 3
    ISSN: 1436-4646
    Keywords: Key words: semidefinite programming – interior-point methods – polynomial complexity – path-following methods – primal-dual methods Mathematics Subject Classification (1991): 65K05, 90C25, 90C30
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Type of Medium: Electronic Resource
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  • 4
    Electronic Resource
    Electronic Resource
    Springer
    Annals of operations research 46-47 (1993), S. 509-539 
    ISSN: 1572-9338
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Notes: Abstract In this paper we deal with global convergence of the affine scaling algorithm for strictly convex QP problems satisfying a dual nondegeneracy condition. By means of the local Karmarkar potential function which was successfully applied to demonstrate global convergence of the affine scaling algorithm for LP, we show global convergence of the algorithm when the step-size 1/8 is adopted without requiring any primal nondegeneracy condition.
    Type of Medium: Electronic Resource
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  • 5
    Electronic Resource
    Electronic Resource
    Springer
    Annals of operations research 62 (1996), S. 325-355 
    ISSN: 1572-9338
    Keywords: Linear programming ; infeasible-interior-point methods ; affine scaling algorithm ; global convergence analysis ; nondegeneracy assumption ; AMS(MOS) 90C05
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Notes: Abstract In this paper, we propose an infeasible-interior-point algorithm for linear programning based on the affine scaling algorithm by Dikin. The search direction of the algorithm is composed of two directions, one for satisfying feasibility and the other for aiming at optimality. Both directions are affine scaling directions of certain linear programming problems. Global convergence of the algorithm is proved under a reasonable nondegeneracy assumption. A summary of analogous global convergence results without any nondegeneracy assumption obtained in [17] is also given.
    Type of Medium: Electronic Resource
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  • 6
    Electronic Resource
    Electronic Resource
    Springer
    Mathematical programming 52 (1991), S. 377-404 
    ISSN: 1436-4646
    Keywords: Linear programming ; interior point methods ; affine scaling methods ; global analysis ; degenerate problems
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract In this paper we show the global convergence of the affine scaling methods without assuming any condition on degeneracy. The behavior of the method near degenerate faces is analyzed in detail on the basis of the equivalence between the affine scaling methods for homogeneous LP problems and Karmarkar's method. It is shown that the step-size 1/8, where the displacement vector is normalized with respect to the distance in the scaled space, is sufficient to guarantee the global convergence of the affine scaling methods.
    Type of Medium: Electronic Resource
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  • 7
    Electronic Resource
    Electronic Resource
    Springer
    Mathematical programming 82 (1998), S. 339-355 
    ISSN: 1436-4646
    Keywords: Linear programming ; Layered-step interior-point method ; Path of centers ; Crossover events
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract The layered-step interior-point algorithm was introduced by Vavasis and Ye. The algorithm accelerates the path following interior-point algorithm and its arithmetic complexity depends only on the coefficient matrixA. The main drawback of the algorithm is the use of an unknown big constant $$\bar \chi _A $$ in computing the search direction and to initiate the algorithm. We propose a modified layered-step interior-point algorithm which does not use the big constant in computing the search direction. The constant is required only for initialization when a well-centered feasible solution is not available, and it is not required if an upper bound on the norm of a primal—dual optimal solution is known in advance. The complexity of the simplified algorithm is the same as that of Vavasis and Ye. © 1998 The Mathematical Programming Society, Inc. Published by Elsevier Science B.V.
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  • 8
    ISSN: 1436-4646
    Keywords: Key words: second-order cone programming – ice-cream cone – interior-point methods – polynomial complexity – path-following methods – primal-dual methods – Newton method
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract. In this paper we study primal-dual path-following algorithms for the second-order cone programming (SOCP) based on a family of directions that is a natural extension of the Monteiro-Zhang (MZ) family for semidefinite programming. We show that the polynomial iteration-complexity bounds of two well-known algorithms for linear programming, namely the short-step path-following algorithm of Kojima et al. and Monteiro and Adler, and the predictor-corrector algorithm of Mizuno et al., carry over to the context of SOCP, that is they have an O(  logε-1) iteration-complexity to reduce the duality gap by a factor of ε, where n is the number of second-order cones. Since the MZ-type family studied in this paper includes an analogue of the Alizadeh, Haeberly and Overton pure Newton direction, we establish for the first time the polynomial convergence of primal-dual algorithms for SOCP based on this search direction.
    Type of Medium: Electronic Resource
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  • 9
    Electronic Resource
    Electronic Resource
    New York : Wiley-Blackwell
    Biopolymers 21 (1982), S. 979-994 
    ISSN: 0006-3525
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The cooperative binding of n-mers to a finite ring, a finite open chain, and an infinite chain is treated in a unified way using the matrix method. For an infinite chain, the implicit closed-form expression (“Scatchard formula”) for the fraction of bound sites obtained by McGhee and von Hippel, is simply rederived using a procedure involving implicit differentiation of the characteristic equation. A variety of models for n-mer binding that incorporate steric hindrance for formulated, and corresponding Scatchard formulas are derived using our procedure.
    Additional Material: 10 Ill.
    Type of Medium: Electronic Resource
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  • 10
    Electronic Resource
    Electronic Resource
    New York : Wiley-Blackwell
    Biopolymers 20 (1981), S. 1399-1411 
    ISSN: 0006-3525
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Heavy meromyosin binding to F-actin saturated with tropomyosin is studied theoretically. The problem is formulated as a special case of n-mer adsorption to a one-dimensional Ising lattice which is divided into m-site-long blocks.
    Additional Material: 9 Ill.
    Type of Medium: Electronic Resource
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