This book addresses the problem of minimizing or maximizing a linear function in the presence of linear equality or inequality constraints.?Methods are provided for modeling complex problems via effective algorithms on modern computers. The general theory and characteristics of optimization problems are presented, along with effective solution algorithms. The book also explores linear programming (LP) and network flows, employing polynomial-time algorithms and various specializations of the simplex method.? Numerous comments and references have been added to this new edition to?reflect the new developments in the field.? New discussions on the recent literature on the geometry of cycling have been added as well as new insights into the nature and construction of examples that admit?cycling.