Books

Author(s)	Book
A. Schrijver Department of Econometrics, Tilburg University	Theory of Linear and Integer Programming John Wiley & Sons, Inc., Chichester, pp.xi+471, 1986 Wiley-Interscience Series in Discrete Mathematics ISBN 0-471-90854-1 Contents Preface 1. Introduction and Preliminaries 2. Problems, Algorithms, and Complexity Part I: Linear Algebra 3. Linear Algebra and Complexity Part II: Lattices and Linear Diophantine Equations 4. Theory of Lattices and Linear Diophantine Equations 5. Algorithms for Linear Diophantine Equations 6. Diophantine Approximation and Basis Reduction Part III: Polyhedra, Linear Inequalities, and Linear Programming 7. Fundamental Concepts and Results on Polyhedra, Linear Inequalities, and Linear Programming 8. The Structure of Polyhedra 9. Polarity, and Blocking and Anti-Blocking Polyhedra 10. Sizes and Theoretical Complexity of Linear Inequalities and Linear Programming 11. The Simplex Method 12. Primal-Dual, Elimination, and Relaxation Methods 13. Khachiyan’s Method for Linear Programming 14. The Ellipsoid Method for Polyhedra more Generally 15. Further Polynomiality Results in Linear Programminh Part IV: Integer Linear Programming 16. Introduction to Integer Linear Programming 17. Estimates in Integer Linear Programming 18. The Complexity of Integer Linear Programming 19. Totally Unimodular Matrices: Fundamental Properties and Examples 20. Recognizing Total Unimodularity 21. Further Theory Related to Total Unimodularity 22. Integral Polyhedra and Total Dual Integrality 23. Cutting Planes 24. Further Methods in Integer Programming References Notation index Author Index Subject Index
Naum Z. Shor, Ukrainian National Academy of Sciences E-mail: nzshor@d120.icyb.kiev.ua	Nondiferentiable Optimization and Polynomial Problems Kluwer Academic Publishers Boston / London / Dordrecht, 1998, 412 pp. $179.00, ISBN 0-7923-4997-0 Contents: 1. Elements of Convex Analysis, Linear Algebra and Graph Theory 2. Subgradient and e-Subgradient Methods 3. Subgradient-Type Methods with Space Dilation 4. Elements of Information and Numerical Complexity of Polynomial Extremal Problems 5. Decomposition Methods Based on Nonsmooth Optimization 6. Algorithms for Constructing Optimal on Volume Ellipsoids and Semidefinite Programming 7. The Role of Ellipsoid Method for Complexity Analysis of Combinatorial Problems 8. Semidefinite Programming Bounds for Extremal Graph Problems 9. Global Minimization of Polynomial Functions and 17-th Hilbert Problem References
Ralph E. Steuer Management Sciences, Brooks Hall, University of Georgia, Athens, Georgia USA 30602-6255 rsteuer@uga.cc.uga.edu	Multiple Criterie Optimization: Theory,Computation and Application John Wiley & Sons, Inc., New York / 1986, xx + 546 pp. ISBN 0-471-88846-X Contents: Preface 1. Introduction 2. Mathematical Background 3. Single Objective Linear Programming 4. Determining all Alternative Optima 5. Comments about Objective Row Parametric Programming 6. Utility Functions, Nondominated Criterion Vectors, and Efficient Points 7. Point Estimate Weighted-Sums Approach 8. Optimal Weighting Vectors, Scaling, and Reduced Feasible Region Methods 9. Vector-Maximum Algorithms 10. Goal Programming 11. Filtering and Set Discretization 12. Multiple Objective Linear Fractional Programming 13. Interactive Procedures 14. Interactive Weighted Tchebycheff Procedure 15. Tchebycheff / Weighted-Sums Implementation 16. Application 17. Future Directions Index
Yousef Saad University of Minesota Department of Computer Science and Engineering 200 Union Street S.E. Minneapolis, MN 55455, USA (saad@cs.umn.edu)	Iterative Methods for Sparse Linear Systems PWS Publishing Company An International Thomson Publishing Company Boston, 1996, xvi +447 pp. ISBN 0-534-9477b-X (hardcover) Contents: Preface Acknowledgments Suggestions for Teaching 1. Background in Linear Algebra 2. Discretization of PDES 3. Sparse Matrices 4. Basic Iterative Methods 5. Projection Methods 6. Krylov Subspace Methods - Part I 7. Krylov Subspace Methods - Part II 8. Methods Related to the Normal Equations 9. Preconditioned Iterations 10. Preconditioning Techniques 11. Parallel Implementatins 12. Parallel Preconditioners 13. Domain Decomposition Methods References Index Review by N. Andrei for Studies in Informatics and Control, vol.6, no.4, December 1997, pp.375-378.