Progress in Mathematical Programming

Interior-Point and Related Methods

Buch | Softcover

158 Seiten

2011 | Softcover reprint of the original 1st ed. 1989
Springer-Verlag New York Inc.
978-1-4613-9619-2 (ISBN)

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The starting point of this volume was a conference entitled "Progress in Mathematical Programming," held at the Asilomar Conference Center in Pacific Grove, California, March 1-4, 1987. The main topic of the conference was developments in the theory and practice of linear programming since Karmarkar's algorithm. There were thirty presentations and approximately fifty people attended. Presentations included new algorithms, new analyses of algorithms, reports on computational experience, and some other topics related to the practice of mathematical programming. Interestingly, most of the progress reported at the conference was on the theoretical side. Several new polynomial algorithms for linear program- ming were presented (Barnes-Chopra-Jensen, Goldfarb-Mehrotra, Gonzaga, Kojima-Mizuno-Yoshise, Renegar, Todd, Vaidya, and Ye). Other algorithms presented were by Betke-Gritzmann, Blum, Gill-Murray-Saunders-Wright, Nazareth, Vial, and Zikan-Cottle. Efforts in the theoretical analysis of algo- rithms were also reported (Anstreicher, Bayer-Lagarias, Imai, Lagarias, Megiddo-Shub, Lagarias, Smale, and Vanderbei).
Computational experiences were reported by Lustig, Tomlin, Todd, Tone, Ye, and Zikan-Cottle. Of special interest, although not in the main direction discussed at the conference, was the report by Rinaldi on the practical solution of some large traveling salesman problems. At the time of the conference, it was still not clear whether the new algorithms developed since Karmarkar's algorithm would replace the simplex method in practice. Alan Hoffman presented results on conditions under which linear programming problems can be solved by greedy algorithms.

1 An Algorithm for Solving Linear Programming Problems in O(n3L) Operations.- 2 A Primal-Dual Interior Point Algorithm for Linear Programming.- 3 An Extension of Karmarkar’s Algorithm and the Trust Region Method for Quadratic Programming.- 4 Approximate Projections in a Projective Method for the Linear Feasibility Problem.- 5 A Locally Weil-Behaved Potential Function and a Simple Newton-Type Method for Finding the Center of a Polytype.- 6 A Note on Comparing Simplex and Interior Methods for Linear Programming.- 7 Pricing Criteria in Linear Programming.- 8 Pathways to the Optimal Set in Linear Programming.

Zusatzinfo	X, 158 p.
Verlagsort	New York, NY
Sprache	englisch
Maße	155 x 235 mm
Themenwelt	Informatik ► Theorie / Studium ► Algorithmen
	Mathematik / Informatik ► Mathematik ► Algebra
	Mathematik / Informatik ► Mathematik ► Analysis
	Mathematik / Informatik ► Mathematik ► Angewandte Mathematik
	Mathematik / Informatik ► Mathematik ► Finanz- / Wirtschaftsmathematik
ISBN-10	1-4613-9619-0 / 1461396190
ISBN-13	978-1-4613-9619-2 / 9781461396192
Zustand	Neuware