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  • 1
    Electronic Resource
    Electronic Resource
    A modification of karmarkar's linear programming algorithm (1986)
    Springer
    Algorithmica 1 (1986), S. 395-407 
    Details
    ISSN: 1432-0541
    Keywords: Linear programming ; Karmarkar's algorithm ; Projected gradient methods ; Least squares
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract We present a modification of Karmarkar's linear programming algorithm. Our algorithm uses a recentered projected gradient approach thereby obviatinga priori knowledge of the optimal objective function value. Assuming primal and dual nondegeneracy, we prove that our algorithm converges. We present computational comparisons between our algorithm and the revised simplex method. For small, dense constraint matrices we saw little difference between the two methods.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01840454
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  • 2
    Electronic Resource
    Electronic Resource
    Symmetric indefinite systems for interior point methods (1993)
    Springer
    Mathematical programming 58 (1993), S. 1-32 
    Details
    ISSN: 1436-4646
    Keywords: Interior point method ; linear programming ; quadratic programming
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract We present a unified framework for solving linear and convex quadratic programs via interior point methods. At each iteration, this method solves an indefinite system whose matrix is $$\left[ {\begin{array}{*{20}c} { - D^{ - 2} } & {A^T } \\ A & 0 \\ \end{array} } \right]$$ instead of reducing to obtain the usualAD 2 A T system. This methodology affords two advantages: (1) it avoids the fill created by explicitly forming the productAD 2 A T whenA has dense columns; and (2) it can easily be used to solve nonseparable quadratic programs since it requires only thatD be symmetric. We also present a procedure for converting nonseparable quadratic programs to separable ones which yields computational savings when the matrix of quadratic coefficients is dense.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01581257
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  • 3
    Electronic Resource
    Electronic Resource
    Interior-point methods for nonconvex nonlinear programming: orderings and higher-order methods (2000)
    Springer
    Mathematical programming 87 (2000), S. 303-316 
    Details
    ISSN: 1436-4646
    Keywords: Key words: nonlinear programming – interior-point methods – nonconvex optimization – predictor-corrector – matrix ordering
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract. The paper extends prior work by the authors on loqo, an interior point algorithm for nonconvex nonlinear programming. The specific topics covered include primal versus dual orderings and higher order methods, which attempt to use each factorization of the Hessian matrix more than once to improve computational efficiency. Results show that unlike linear and convex quadratic programming, higher order corrections to the central trajectory are not useful for nonconvex nonlinear programming, but that a variant of Mehrotra’s predictor-corrector algorithm can definitely improve performance.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s101070050116
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  • 4
    Electronic Resource
    Electronic Resource
    An Interior-Point Algorithm for Nonconvex Nonlinear Programming (1999)
    Springer
    Computational optimization and applications 13 (1999), S. 231-252 
    Details
    ISSN: 1573-2894
    Keywords: nonlinear programming ; interior-point methods ; nonconvex optimization
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Notes: Abstract The paper describes an interior-point algorithm for nonconvex nonlinear programming which is a direct extension of interior-point methods for linear and quadratic programming. Major modifications include a merit function and an altered search direction to ensure that a descent direction for the merit function is obtained. Preliminary numerical testing indicates that the method is robust. Further, numerical comparisons with MINOS and LANCELOT show that the method is efficient, and has the promise of greatly reducing solution times on at least some classes of models.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1008677427361
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  • 5
    Electronic Resource
    Electronic Resource
    Extension of Piyavskii's Algorithm to Continuous Global Optimization (1999)
    Springer
    Journal of global optimization 14 (1999), S. 205-216 
    Details
    ISSN: 1573-2916
    Keywords: Global optimization ; Lipschitz continuity ; Piyavskii's algorithm ; Uniform Continuity
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We use the simple, but little-known, result that a uniformly continuous function on a convex set is ε-Lipschitz (as defined below) to extend Piyavskii's algorithm for Lipschitz global optimization to the larger domain of continuous (not-necessarily-Lipschitz) global optimization.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1008395413111
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  • 6
    Book
    Book
    Linear Programming : foundations and extensions; 4 (1996)
    Boston u.a. :Kluwer Academic Publishers,
    Details
    Title: Linear Programming : foundations and extensions; 4
    Author: Vanderbei, Robert J.
    Publisher: Boston u.a. :Kluwer Academic Publishers,
    Year of publication: 1996
    Pages: 418 S.
    Series Statement: International series in operations research and management science 4
    Type of Medium: Book
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  • 7
    Book
    Book
    Linear programming : foundations and extensions; 196 (2014)
    New York, N.Y. [u.a.] :Springer,
    Details
    Title: Linear programming : foundations and extensions; 196
    Author: Vanderbei, Robert J.
    Edition: 4. ed.
    Publisher: New York, N.Y. [u.a.] :Springer,
    Year of publication: 2014
    Pages: XXII, 414 S. : , graph. Darst.
    Series Statement: International series in operations research & management science 196
    ISBN: 978-1-4614-7629-0
    Type of Medium: Book
    Language: English
    URL: https://zbmath.org/?q=an:1299.90243
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  • 8
    Book
    Book
    Linear programming /; 114 (2008)
    New York, NY :Springer,
    Details
    Title: Linear programming /; 114
    Author: Vanderbei, Robert J.
    Edition: 3. ed.
    Publisher: New York, NY :Springer,
    Year of publication: 2008
    Pages: XIII, 464 S. : , Ill., graph. Darst. ; , 235 mm x 155 mm
    Series Statement: International series in operations research & management science 114
    ISBN: 0-387-74387-1 , 978-0-387-74387-5
    Type of Medium: Book
    Language: English
    URL: 01  (lizenzfrei)
    URL: 04
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  • 9
    Book
    Book
    Real and Convex Analysis / (2013)
    Boston, MA :Springer,
    Details
    Title: Real and Convex Analysis /
    Author: Çınlar, Erhan
    Contributer: Vanderbei, Robert J.
    Publisher: Boston, MA :Springer,
    Year of publication: 2013
    Pages: 23 illus., 2 illus. in color
    Series Statement: Undergraduate texts in mathematics
    ISBN: 978-1-461-45257-7 , 978-1-461-45256-0
    Type of Medium: Book
    Language: English
    URL: http://www.zentralblatt-math.org/zmath/en/advanced/?q=an:pre06085888&format=complete
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