Understanding and Using Linear ProgrammingSpringer Science & Business Media, 5. 10. 2006 - 226 strán (strany) This is an introductory textbook of linear programming, written mainly for students of computer science and mathematics. Our guiding phrase is, “what everytheoreticalcomputerscientistshouldknowaboutlinearprogramming.” The book is relatively concise, in order to allow the reader to focus on the basic ideas. For a number of topics commonly appearing in thicker books on the subject, we were seriously tempted to add them to the main text, but we decided to present them only very brie?y in a separate glossary. At the same time, we aim at covering the main results with complete proofs and in su?cient detail, in a way ready for presentation in class. One of the main focuses is applications of linear programming, both in practice and in theory. Linear programming has become an extremely ?- ible tool in theoretical computer science and in mathematics. While many of the ?nest modern applications are much too complicated to be included in an introductory text, we hope to communicate some of the ?avor (and excitement) of such applications on simpler examples. |
Obsah
Preface | 1 |
Examples | 11 |
Integer Programming and LP Relaxation | 28 |
The Simplex Method | 77 |
Duality of Linear Programming | 81 |
Not Only the Simplex Method | 105 |
More Applications | 131 |
Software and Further Reading 193 | 192 |
Glossary | 201 |
| 217 | |
| 220 | |
Iné vydania - Zobraziť všetky
Časté výrazy a frázy
algorithm auxiliary linear program ball basic feasible solution BP-exact central path coefficients Colonel Blotto column components compute consider constraints convex sets d-intervals define denote dual linear program dual simplex method duality theorem edges ellipsoid method entering variable equational form exactly example Farkas lemma feasible basis infeasible integer program interior point methods intersection leaving variable linear inequalities linear subspace linearly independent LP relaxation makespan matching matrix maximize subject maximum minimize mixed strategy Nash equilibrium nonnegative solution nonzero objective function optimal solution optimum original linear program payoff pivot rule pivot step polyhedron polynomial polytope primal linear program problem program in equational proof prove real numbers satisfies Section semidefinite simplex method simplex tableau smallest enclosing ball solving sparse solution subject to Ax system Ax system of linear upper bound vector vertex cover vertices