Linear Programming And Network Flows

The book addresses the problem of minimizing or maximizing a linear function in the presence of linear equality or inequality constraints. The general theory and characteristics of optimization problems are presented, along with effective solution algorithms. It explores linear programming and network flows, employing polynomial-time algorithms and various specializations of the simplex method. The text also includes many numerical examples to illustrate theory and techniques. · linear algebra, convex analysis, and polyhedral sets · the simplex method · starting solution and convergence · special simplex implementations and optimality conditions · duality and sensitivity analysis · the decomposition principle · complexity of the simplex algorithm and polynomial algorithms · minimal cost network flows · the transportation and assignment problems · the out-of-kilter algorithm · maximal flow, shortest path, multicommodity flow, and network synthesis problems