Understanding and Using Linear ProgrammingThis 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. |
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algorithm auxiliary linear program ball basic feasible solution BP-exact central path coefficients Colonel Blotto column components convex polyhedron convex sets d-intervals define dual linear program duality theorem edge ellipsoid method entering variable equational form exactly example Farkas lemma feasible basis finitely geometric infeasible integer program interior point methods intersection leaving variable linear algebra linear equations linear inequalities linear subspace linearly independent LP relaxation matching mathematical matrix maximize cx subject Maximize subject maximum minimize mixed strategy Nash equilibrium nonbasic variables nonzero objective function optimal solution optimum original linear program payoff pivot rule pivot step polynomial polytope possible problem program in equational proof prove real number satisfies Section simplex method simplex tableau smallest enclosing ball solving sparse solution subject to Ax system Ax system of linear theory tion upper bound vector vertex cover vertices