Linear Optimization and Extensions - Manfred Padberg

. .

Résumé :
I was pleasantly surprised when I was asked by Springer-Verlag to prepare a second edition of this volume on Linear Optimization and Extensions, which - not exactly contrary to my personal expectations - has apparently been accepted reasonably weIl by the global optimization community. My objective in putting this book together was originally - and still is - to detail the major algorithmic ideas in linear optimization that have evolved in the past fifty years or so and that have changed the historical optimization landscape in substantial ways - both theoretically and computationally. While I may have overlooked the importance of some very recent developments - the work by Farid Alizadeh which generalizes linear programming to sem i-definite programming is perhaps a candidate for one of my omissions - I think that major new breakthraughs on those two fronts that interest me - theory and computation - have not occurred since this book was published originally. As a consequence I have restricted myself to a thorough re-working of the original manuscript with the goal of making it more readable. Of course, I have taken this opportunity to correct a few Sch?nheitsfehler of the first edition and to add some illustrations. The index to this volume has been extended substantially - to permit a hurried reader a quicker glance at the wealth of topics that were covered nevertheless already in the first edition. As was the case with the first edition, Dr.

Sommaire:
The Linear Programming Problem.- Basic Concepts.- Five Preliminaries.- Simplex Algorithms.- Primal-Dual Pairs.- Analytical Geometry.- Projective Algorithms.- Ellipsoid Algorithms.- Combinatorial Optimization: An Introduction.