Nonlinear Optimization with Engineering ApplicationsThis book, like its companion volume Nonlinear Optimization with Financial Applications, is an outgrowth of undergraduate and po- graduate courses given at the University of Hertfordshire and the University of Bergamo. It deals with the theory behind numerical methods for nonlinear optimization and their application to a range of problems in science and engineering. The book is intended for ?nal year undergraduate students in mathematics (or other subjects with a high mathematical or computational content) and exercises are provided at the end of most sections. The material should also be useful for postg- duate students and other researchers and practitioners who may be c- cerned with the development or use of optimization algorithms. It is assumed that readers have an understanding of the algebra of matrices and vectors and of the Taylor and mean value theorems in several va- ables. Prior experience of using computational techniques for solving systems of linear equations is also desirable, as is familiarity with the behaviour of iterative algorithms such as Newton’s methodfor nonlinear equations in one variable. Most of the currently popular methods for continuous nonlinear optimization are described and given (at least) an intuitive justi?cation. Relevant convergence results are also outlined and we provide proofs of these when it seems instructive to do so. This theoretical material is complemented by numerical illustrations which give a ?avour of how the methods perform in practice. |
Contents
| 1 | |
Onevariable Optimization | 11 |
Applications in n Variables | 33 |
nVariable Unconstrained Optimization | 41 |
Direct Search Methods | 53 |
Computing Derivatives | 63 |
The Steepest Descent Method | 75 |
Weak Line Searches and Convergence | 83 |
Global Unconstrained Optimization | 147 |
Equality Constrained Optimization | 155 |
Linear Equality Constraints | 169 |
Penalty Function Methods | 183 |
Sequential Quadratic Programming | 197 |
Inequality Constrained Optimization | 211 |
Extending Equality Constraint Methods | 225 |
Barrier Function Methods | 239 |
Newton and Newtonlike Methods | 91 |
QuasiNewton Methods | 107 |
Conjugate Gradient Methods | 119 |
A Summary of Unconstrained Methods | 131 |
Optimization with Restrictions | 133 |
LargerScale Problems | 141 |
Interior Point Methods | 249 |
A Summary of Constrained Methods | 259 |
The OPTIMA Software | 261 |
| 273 | |
| 277 | |
Other editions - View all
Nonlinear Optimization with Engineering Applications Michael Bartholomew-Biggs No preview available - 2010 |
Nonlinear Optimization with Engineering Applications Michael Bartholomew-Biggs No preview available - 2008 |
Nonlinear Optimization with Engineering Applications Michael Bartholomew-Biggs No preview available - 2008 |
Common terms and phrases
AL-SQP AL-SUMT algorithm applied approach approximation augmented Lagrangian Bartholomew-Biggs BFGS bisection method calculation Chapter conjugate gradient method constrained problems contours convergence cost data points DIMENSION(1:n doublet equations estimate Exercises F(xk feasible point function F(x function value Hence Hessian Hessian matrix Hk+1 implementation inequality constraints INTEGER INTENT(in INTENT(out iterations and function itns/fns itns/fns Lagrange multipliers least squares linear matrix Minimize F(x minimum of F(x Newton method Nonlinear Optimization numbers of iterations objective function obtained optimality conditions Optimization with Engineering optimum P-SUMT parameter penalty function perfect line search performance positive-definite problem Minimize Problem TD1 Problem VLS2 Problems TD1–OC2 quadratic function quasi-Newton methods reduced-gradient satisfy search direction secant method Solutions of Problem solve SOLVER Springer Science+Business Media starting guess steepest descent subproblem SUBROUTINE Table TD1a TLS1 update variables vector VLS1 weak line search Wolfe conditions xk+1 zero