02944nam 22007455a 450 99101519316033212010-09-073-03719-593-210.4171/093(CKB)3710000000953859(CH-001817-3)119-100820(PPN)178155810(DE-4084)10.4171/093(EXLCZ)99371000000095385920100907j20100907 fy 0engurnn|mmmmamaatxtrdacontentcrdamediacrrdacarrierNonlinear Discrete Optimization ;An Algorithmic TheoryEMS Press20101 online resource (147 pages)Zurich Lectures in Advanced Mathematics (zlam)132943-4971This monograph develops an algorithmic theory of nonlinear discrete optimization. It introduces a simple and useful setup which enables the polynomial time solution of broad fundamental classes of nonlinear combinatorial optimization and integer programming problems in variable dimension. An important part of this theory is enhanced by recent developments in the algebra of Graver bases. The power of the theory is demonstrated by deriving the first polynomial time algorithms in a variety of application areas within operations research and statistics, including vector partitioning, matroid optimization, experimental design, multicommodity flows, multi-index transportation and privacy in statistical databases. The monograph is intended for graduate students and researchers. It is accessible to anyone with standard undergraduate knowledge and mathematical maturity.Linear programmingbicsscOperations research, mathematical programmingmscCombinatoricsmscLinear and multilinear algebra; matrix theorymscComputer sciencemscLinear programmingOperations research, mathematical programmingCombinatoricsLinear and multilinear algebra; matrix theoryComputer science05Axxmsc05Cxxmsc05Dxxmsc05Exxmsc11Dxxmsc11Hxxmsc11Pxxmsc13Pxxmsc14Qxxmsc15Axxmsc15Bxxmsc51Mxxmsc52Axxmsc52Bxxmsc52Cxxmsc62Hxxmsc62Kxxmsc62Qxxmsc65Cxxmsc68Qxxmsc68Rxxmsc68Wxxmsc90Bxxmsc90CxxmscOnnaut2014681DE-4084BOOK9910151931603321Nonlinear Discrete Optimization4805316UNINA