Katta G. Murty ... 502 pages - Publisher: Springer; 2010 edition (March 14, 2010)
Language: English - ASIN: B008BA5X7Q
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.
From Back Cover: 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.
