Optimization for Decision Making - Murty, Katta G

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Résumé :
Optimization for Decision Making: Linear and Quadratic Models is a first-year graduate level text that illustrates how to formulate real world problems using linear and quadratic models; how to use efficient algorithms - both old and new - for solving these models; and how to draw useful conclusions and derive useful planning information from the output of these algorithms. While almost all the best known books on LP are essentially mathematics books with only very simple modeling examples, this book emphasizes the intelligent modeling of real world problems, and the author presents several illustrative examples and includes many exercises from a variety of application areas. Additionally, where other books on LP only discuss the simplex method, and perhaps existing interior point methods, this book also discusses a new method based on using the sphere which uses matrix inversion operations sparingly and may be well suited to solving large-scale LPs, as well as those that may not have the property of being very sparse. Individual chapters present a brief history of mathematical modeling; methods for formulating real world problems; three case studies that illustrate the need for intelligent modeling; classical theory of polyhedral geometry that plays an important part in the study of LP; duality theory, optimality conditions for LP, and marginal analysis; variants of the revised simplex method; interior point methods; sphere methods; and extensions of sphere method to convex and nonconvex quadratic programs and to 0-1 integer programs through quadratic formulations. End of chapter exercises are provided throughout, with additional exercises available online.

Sommaire:
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.