Linear Equations, Inequalities, Linear Programming: A Brief Historical Overview.- Formulation Techniques Involving Transformations of Variables.- Intelligent Modeling Essential to Get Good Results.- Polyhedral Geometry.- Duality Theory and Optimality Conditions for LPs.- Revised Simplex Variants of the Primal and Dual Simplex Methods and Sensitivity Analysis.- Interior Point Methods for LP.- Sphere Methods for LP.- Quadratic Programming Models.
Linear programming (LP), modeling, and optimization are very much the fundamentals of OR, and no academic program is complete without them. No matter how highly developed one's LP skills are, however, if a fine appreciation for modeling isn't developed to make the best use of those skills, then the truly 'best solutions' are often not realized, and efforts go wasted.
Katta Murty studied LP with George Dantzig, the father of linear programming, and has written the graduate-level solution to that problem. While maintaining the rigorous LP instruction required, Murty's new book is unique in his focus on developing modeling skills to support valid decision making for complex real world problems. He describes the approach as 'intelligent modeling and decision making' to emphasize the importance of employing the best expression of actual problems and then applying the most computationally effective and efficient solution technique for that model.
Presents advanced linear programming with a unique focus on modeling techniques
Two chapters on entirely new algorithms and their results
Author website with additional exercises and mathematical results of new algorithms covered in book