LDR 03221 2200349 4500 010 _a9780898716863 _bbr. 090 _a17004 101 _aeng 102 _aUS 100 _a20181112 frey50 200 _aThe linear complementarity problem _bM _fRichard W. Cottle, Jong-Shi Pang, Richard E. Stone 205 _arevised ed. of the 1992 original 210 _a Philadelphia _cSIAM _dcop. 2009 215 _a1 vol. (xxvii-761 p.) _cill. _d24 225 _9169327 _aClassics in applied mathematics 320 _aBibliogr. p. 701-751. Index 330 _aIn this book, the authors attempt to include every major aspect of the LCP. They cover all topics of traditional and current importance, presenting them in a style consistent with a contemporary point of view, and providing the most comprehensive available list of references. This monograph is intended for readers with some background in linear algebra, linear programming and real analysis. All seven chapters of this volume are divided into sections. The opening chapter sets forth a precise statement of the linear complementarity problem and then offers a selection of settings in which such problems arise. Chapter 1 includes a number of other topics, such as equivalent formulations and generalizations of the LCP. The essential background materials needed for the rest of the book is collected in Chapter 2. Chapter 3 is concerned with questions on the existence and multiplicity to linear complementarity problems. Chapter 4 covers the better-known pivoting algorithms (notably principal pivoting methods and Lemkeās method) for solving linear complementarity problems of various kinds; parametric versions are also presented. Algorithms of the latter sort (e.g., matrix splitting methods, a damped Newton method, and interior-point methods) are treated in Chapter 5. Chapter 6 offers a more geometric view of the linear complementarity problem. The concluding Chapter 7 focuses on sensitivity and stability analysis, the study of how small changes in the data affect various aspects of the problem (zbMath) 410 _9173967 _aSIAM _tClassics in applied mathematics 676 _a2010 686 _20 _9166735 _a90-01 _bOperations research, mathematical programming _xInstructional exposition (textbooks, tutorial papers, etc.) 686 _20 _9166778 _a90C33 _bOperations research, mathematical programming -- Mathematical programming _xComplementarity and equilibrium problems and variational inequalities (finite dimensions) 686 _20 _9166769 _a90C20 _bOperations research, mathematical programming -- Mathematical programming _xQuadratic programming 686 _20 _9165765 _a65K05 _bNumerical analysis -- Mathematical programming, optimization and variational techniques _xMathematical programming methods 700 _4070 _aCottle _bRichard Warren _f1934- _9183276 701 _4070 _aPang _bJong-Shi _9183277 701 _4070 _aStone _bRichard E. _9183278 856 _uhttps://mathscinet.ams.org/mathscinet-getitem?mr=3396730 _zMSN 856 _uhttps://zbmath.org/?q=an%3A1192.90001 _zzbMath 905 _aaw _b2018 906 _aaw _b2018-11-12 001 17004 995 _f12529-01 _xachat Ebsco _918689 _cCMI _20 _k90 COT _o0 _eSalle R _z103.20 _bCMI