Linear Programming Computation

Organized into two volumes. this book represents a real breakthrough in the field of linear programming (LP). The first volume addresses fundamentals, including geometry of feasible region, simplex method, implementation of simplex method, duality and dual simplex method, sensitivity analysis and parametric LP, generalized simplex method, decomposition method, interior-point method and integer LP method, as well as reflects the state of art by highlighting new results, such as efficient primal and dual pivot rules, primal and dual Phase-I methods. The second volume introduces contributions of the author himself, such as reduced and D-reduced-simplex methods, generalized reduced and dual reduced simplex methods, deficient-basis and dual deficient-basis-simplex methods, and face and dual face methods with Cholesky factorization, as well as with LU factorization. As a monograph, this book is a rare work in LP, containing many noval ideas and methods, supported by complete computational results. As revealed from the perspective of theory, the most recently achieved results, such as reduced and D-reduced simplex methods, as well as ILP solvers--- controlled-cut and controlled-branch methods, are very significant and promising, though there are no computational results available at this stage. With a focus on computation, the content of this book ranges from simple to profound, clear and fresh. In particular, all algorithms are accompanied by examples for demonstration whenever possible. As a milestone of LP, this book is an indispensable tool for undergraduate and graduate students, teachers, practitioners and researchers, in LP and related fields.