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  • 1
    Electronic Resource
    Electronic Resource
    Springer
    Mathematical programming 56 (1992), S. 189-222 
    ISSN: 1436-4646
    Keywords: 65H10 ; 65K05 ; 65K10 ; Linearℓ 1 estimation ; linear programming ; interior-point algorithm ; simplex method ; least absolute value regression ; affine scaling method ; Karmarkar
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract Recently, various interior point algorithms related to the Karmarkar algorithm have been developed for linear programming. In this paper, we first show how this “interior point” philosophy can be adapted to the linear ℓ1 problem (in which there are no feasibility constraints) to yield a globally and linearly convergent algorithm. We then show that the linear algorithm can be modified to provide aglobally and ultimatelyquadratically convergent algorithm. This modified algorithm appears to be significantly more efficient in practise than a more straightforward interior point approach via a linear programming formulation: we present numerical results to support this claim.
    Type of Medium: Electronic Resource
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  • 2
    Electronic Resource
    Electronic Resource
    Springer
    Mathematical programming 45 (1989), S. 373-406 
    ISSN: 1436-4646
    Keywords: 65K05 ; 90C20 ; 65K10 ; 65F30 ; Quadratic programming ; large sparse minimization ; active set methods ; trust region methods ; sparse Cholesky factorization updates ; simple bounds ; box constraints
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract We show how a direct active set method for solving definite and indefinite quadratic programs with simple bounds can be efficiently implemented for large sparse problems. All of the necessary factorizations can be carried out in a static data structure that is set up before the numeric computation begins. The space required for these factorizations is no larger than that required for a single sparse Cholesky factorization of the Hessian of the quadratic. We propose several improvements to this basic algorithm: a new way to find a search direction in the indefinite case that allows us to free more than one variable at a time and a new heuristic method for finding a starting point. These ideas are motivated by the two-norm trust region problem. Additionally, we also show how projection techniques can be used to add several constraints to the active set at each iteration. Our experimental results show that an algorithm with these improvements runs much faster than the basic algorithm for positive definite problems and finds local minima with lower function values for indefinite problems.
    Type of Medium: Electronic Resource
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  • 3
    Electronic Resource
    Electronic Resource
    Springer
    Mathematical programming 53 (1992), S. 17-44 
    ISSN: 1436-4646
    Keywords: 65H10 ; 65K05 ; 65K10 ; Constrained optimization ; equality constraints ; numerical optimization ; quasi-Newton method ; secant method ; sequential quadratic programming ; SQP-method ; augmented Lagrangian method ; penalty function methods
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract We derive new quasi-Newton updates for the (nonlinear) equality constrained minimization problem. The new updates satisfy a quasi-Newton equation, maintain positive definiteness on the null space of the active constraint matrix, and satisfy a minimum change condition. The application of the updates is not restricted to a small neighbourhood of the solution. In addition to derivation and motivational remarks, we discuss various numerical subtleties and provide results of numerical experiments.
    Type of Medium: Electronic Resource
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  • 4
    Electronic Resource
    Electronic Resource
    Weinheim : Wiley-Blackwell
    Zeitschrift für anorganische Chemie 52 (1907), S. 368-396 
    ISSN: 0863-1778
    Keywords: Chemistry ; Inorganic Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Es wurde eine bequeme Methode zur elektrolytischen Darstellung der Vanadisalze ausgearbeitet.Es wurde das elektromotorische Verhalten gelöster Vanadinsalze in verschiedenen Oxydationsstufen untersucht.Es wurde qualitativ das Verhalten der Vanadinsalze zu verschiedenen Oxydations- und Reduktionsmitteln, sowie zu Bikarbonatlösungen untersucht.Es wurde quantitativ die Reaktionsgeschwindigkeit zwischen Vanadi- und Silbersulfat, sowie der katalytische Einflufs von Eisen- und Kupfersalzen auf diese Reaktion untersucht.Bei Gegenwart von Kupfersalzen wird in dieser Reaktion eine Anfangsbeschleunigung beobachtet, die mit einer amorphen Ausscheidung des Silbers Hand in Hand geht.Es wurden die qualitativen Methoden zum Nachweis von Vanadi- und Vanadoverbindungen kritisch besprochen.
    Additional Material: 11 Ill.
    Type of Medium: Electronic Resource
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  • 5
    Electronic Resource
    Electronic Resource
    Weinheim : Wiley-Blackwell
    Zeitschrift für anorganische Chemie 232 (1937), S. 319-324 
    ISSN: 0863-1786
    Keywords: Chemistry ; Inorganic Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: 1. Die günstigsten Bedingungen für die Reaktion zwischen Natriumcarbonatlösung und einem gefällten käuflichen Tricalciumphosphat wurden bestimmt und mit denen für Knochenasche verglichen.
    Additional Material: 3 Ill.
    Type of Medium: Electronic Resource
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  • 6
    ISSN: 0044-2313
    Keywords: Zintl anions ; extraction of alloys ; homo atomic nine vertex polyhedra ; crystal structure ; paramagnetism ; Chemistry ; Inorganic Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Description / Table of Contents: Homoatomare neunkernige Polyeder mit Elementen der Gruppe XIV. Die Kristallstrukturen und paramagnetischen Eigenschaften von [K-(2,2,2-crypt)]6E9E9 · 1.5-Ethylendiamin · 0.5 Toluol, E = Sn and Pb1)Die Extraktionen von Legierungen der nominalen Zusammensetzung „KE2.25“ mit Ethylendiamin (en), (2,2,2)crypt und Toluol (tol) ergeben in guten Ausbeuten paramagnetische Verbindungen der Zusammensetzung [K-(2,2,2-crypt)]6E9E9 · 1.5 en · 0.5 tol (E = Sn (2 b), Pb (2 c)). Einkristall-Röntgenstrukturanalysen zeigen, daß zwei unterschiedliche E9 Cluster pro asymmetrischer Einheit der Elementarzelle vorliegen mit Konfigurationen von verzerrten, dreifach überkappten trigonal prismatischen Polyedern. 2 b: Raumgruppe P21/c (Nr. 14), Z = 4, a = 28.042(8), b = 23.527(5), c = 27.703(8) Å, β = 93.46(2)°; 2 c: Raumgruppe P21/c (Nr. 14), Z = 4, a = 28.356(8), b = 23.757 (5), c = 27.885(8) Å, β = 94.01(2)°.
    Notes: The extractions of alloys of the nominal composition “KE2.25” with ethylenediamine (en), (2,2,2)crypt, and toluene (tol) lead in good yields to paramagnetic compounds of the composition [K-(2,2,2-crypt)]6E9E9 · 1.5 en · 0.5 tol (E = Sn (2 b), Pb (2 c)). X-ray single crystal structure analyses show that two different E9 clusters per asymmetric unit are present with configurations of distorted tricapped trigonal prismatic polyhedra. 2 b: space group P21/c (No. 14), Z = 4, a = 28.042(8), b = 23.527(5), c = 27.703(8) Å, β = 93.46(2)°; 2 c: space group P21/c (No. 14), Z = 4, a = 28.356(8), b = 23.757(5), c = 27.885(8) Å, β = 94.01(2)°.
    Additional Material: 4 Ill.
    Type of Medium: Electronic Resource
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  • 7
    Electronic Resource
    Electronic Resource
    Weinheim : Wiley-Blackwell
    Berichte der deutschen chemischen Gesellschaft 72 (1939), S. 1866-1869 
    ISSN: 0365-9631
    Keywords: Chemistry ; Inorganic Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Type of Medium: Electronic Resource
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