Building and solving mathematical programming models in engineering and science (Q2768983)

Building and Solving Mathematical Programming Models is a very appropriate title for this book. The authors present mathematical programming models and solution techniques of the linear, integer and nonlinear variety. Plenty of examples are given and the use of a modeling language (GAMS) is demonstrated. NEWLINENEWLINENEWLINEThe book consists of four parts. In the first the authors present typical linear, (mixed) integer and nonlinear programming models and a number of modeling exercises. The second part covers fundamental methods of mathematical programming in six chapters entitled An Introduction to Linear Programming, Understanding the Set of All Feasible Solutions, Solving the Linear Programming Problem, Mixed Integer Linear Programming, Optimality and Duality in Nonlinear Programming, and Computational Methods for Nonlinear Programming. In these chapters the mathematical background of mathematical programming is described and numerous numerical examples given to illustrate the mathematical concepts. Proofs of some results are given (the main theorem of linear programming, weak duality, validity of pivots, optimality condition for linear programming, global optimality for convex nonlinear programming problems, KKT sufficient conditions and Lagrangian duality). The methods discussed are primal and dual simplex algorithm, branch and bound, KKT conditions, Newton, secant and quadratic approximation for line search, steepest descent, Newton, quasi-Newton (DFP and BFGS formula) methods for unconstrained optimization and Lagrangian, penalty function, and barrier methods for constrained optimization. An interior point method for linear programming is also presented. NEWLINENEWLINENEWLINEPart III contains two chapters. In Chapter 10 the GAMS package is introduced and its modeling language explained. In Chapter 11 the examples of Part I are modeled and solved using GAMS. Part IV, Applications, has another chapter on applications in which practical problems from various fields are discussed and GAMS models are shown. Chapter 13 explains some standard modeling tricks. Appendix A contains some material on linear systems and their solution. NEWLINENEWLINENEWLINEThe book is suitable for mathematical programming undergraduate courses in engineering, science or commerce with focus on modeling and solution methods. It is not a book for mathematicians or mathematics students.