Practical Mathematical Optimization: An Introduction to Basic Optimization Theory and Classical and New Gradient-Based Algorithms
It is intended that this book be used in senior- to graduate-level semester courses in optimization, as offered in mathematics, engineering, com puter science and operations research departments. Hopefully this book will also be useful to practising professionals in the workplace. The contents of the book represent the fundamental optimization mate rial collected and used by the author, over a period of more than twenty years, in teaching Practical Mathematical Optimization to undergradu ate as well as graduate engineering and science students at the University of Pretoria. The principal motivation for writing this work has not been the teaching of mathematics per se, but to equip students with the nec essary fundamental optimization theory and algorithms, so as to enable them to solve practical problems in their own particular principal fields of interest, be it physics, chemistry, engineering design or business eco nomics. The particular approach adopted here follows from the author's own personal experiences in doing research in solid-state physics and in mechanical engineering design, where he was constantly confronted by problems that can most easily and directly be solved via the judicious use of mathematical optimization techniques. This book is, however, not a collection of case studies restricted to the above-mentioned specialized research areas, but is intended to convey the basic optimization princi ples and algorithms to a general audience in such a way that, hopefully, the application to their own practical areas of interest will be relatively simple and straightforward.
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Practical Mathematical Optimization: An Introduction to Basic Optimization ...
Limited preview - 2005
applied approximation basic computed conjugate gradient method conjugate with respect Consider constrained minimum constrained optimization constraint functions Contour representation convergence convex set corresponding denoted descent direction equality constrained problem equality constraints ETOPC evaluations feasible region Fletcher Fletcher-Reeves follows function value given gives x2 global minimum global optimum gradient vector gradient-based Hessian matrix inequality constraints iteration KKT conditions Lagrange multipliers large number LFOP LFOPC line search line search descent linear local minimum mathematical optimization maximum minimize/(x mutually conjugate Newton Newton's method noise objective function obtained optimization algorithm optimization problem outgoing variable penalty function primal problem proof quadratic function saddle point satisfied search direction shown in Figure simplex method Snyman and Fatti solving spherical quadratic SQSD method starting point stationary points steepest descent strong local minimum subproblems Substituting tableau test problems Theorem tion Torn and Zilinskas unconstrained minimization vfc+1 xfc+1 zero