SCALES:INTRODUCTION NON-LINEAR, OPTIMIZATION RPTIn this textbook the author concentrates on presenting the main core of methods in non-linear optimization that have evolved over the past two decades. It is intended primarily for actual or potential practising optimizer who need to know how different methods work, how to select methods for the job in hand and how to use the chosen method. While the level of mathematical rigour is not very high, the book necessarily contains a considerable amount of mathematical argument and pre-supposes a knowledge such as would be attained by someone reaching the end of the second year of an undergraduate course in physical science, engineering or computational mathematics. The main emphasis is on linear algebra, and more advanced topics are discussed briefly where relevant in the text. The book will appeal to a range of students and research workers working on optimization problems in such fields as applied mathematics, computer science, engineering, business studies, economics and operations research. |
Other editions - View all
Common terms and phrases
a₁ active set algorithm Amax approximation AT(x b₁ Bk+1 Broyden's family bx+1 Ck+1 compute condition number conjugate gradient methods contour curvature descent direction eigenvalues equality constraints exact linear search factorization feasible figure first-order Fk+1 Fletcher formula function value Gauss-Newton Gill and Murray Golden Section search gradient evaluations gradient vector gtol Hessian matrix Hk Agk Hk+1 inequality constraints input xo interpolation interval of uncertainty interval reduction Lagrange multiplier Lagrangian methods modified Newton method non-linear number of iterations objective function obtained optimization orthogonal penalty function positive definite possible problem quadratic function quadratic termination quasi-Newton methods rate of convergence saddle point satisfy scalar search vector second derivatives second-order set ak+1 solve stationary point steepest descent strong minimum subspace sufficiently symmetric Taylor series techniques Uk+1 update xk+1 zero