Название: Linear Programming Computation, 2nd Edition
Автор: Ping-Qi Pan
Издательство: Springer
Год: 2023
Страниц: 739
Язык: английский
Формат: pdf (true), epub
Размер: 34.6 MB

Linear programming (LP) founded by Dantzig might be one of the most well-known and widely used mathematical tools in the world. As a branch of optimization, it serves as the most important cornerstone of operations research, decision science, and management science.

Being both thoughtful and informative, it focuses on reflecting and promoting the state of the art by highlighting new achievements in LP. This new edition is organized in two volumes. The first volume addresses foundations of LP, including the geometry of feasible region, the simplex method and its implementation, duality and the dual simplex method, the primal-dual simplex method, sensitivity analysis and parametric LP, the generalized simplex method, the decomposition method, the interior-point method and integer LP method. The second volume mainly introduces contributions of the author himself, such as efficient primal/dual pivot rules, primal/dual Phase-I methods, reduced/D-reduced simplex methods, the generalized reduced simplex method, primal/dual deficient-basis methods, primal/dual face methods, a new decomposition principle, etc.

Many important improvements were made in this edition. The first volume includes new results, such as the mixed two-phase simplex algorithm, dual elimination, fresh pricing scheme for reduced cost, bilevel LP models and intercepting of optimal solution set. In particular, the chapter Integer LP Method was rewritten with great gains of the objective cutting for new ILP solvers {it controlled-cutting/branch} methods, as well as with an attractive implementation of the controlled-branch method.