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Books > Computing & IT > General theory of computing > Data structures
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Progress in Mathematical Programming - Interior-Point and Related Methods (Paperback, Softcover reprint of the original 1st ed. 1989)
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Progress in Mathematical Programming - Interior-Point and Related Methods (Paperback, Softcover reprint of the original 1st ed. 1989)
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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.
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