Practical Methods of Optimization
This established textbook is noted for its coverage of optimization methods that are of practical importance. It provides a thorough treatment of standard methods such as linear and quadratic programming, Newton-like methods and the conjugate gradient method. The theoretical aspects of the subject include an extended treatment of optimality conditions and the significance of Lagrange multipliers. The relevance of convexity theory to optimization is also not neglected. A significant proportion of the book is devoted to the solution of nonlinear problems, with an authoritative treatment of current methodology. Thus state of the art techniques such as the BFGS method, trust region methods and the SQP method are described and analysed. Other features are an extensive treatment of nonsmooth optimization and the L_1 penalty function. Contents Part 1 Unconstrained Optimization Part 2 Constrained Optimization* Introduction* Structure of Methods* Newton-like Methods* Conjugate Direction Methods* Restricted Step Methods* Sums of Squares and Nonlinear Equations* Introduction* Linear Programming* The Theory of Constrained Optimization* Quadratic Programming* General Linearly Constrained Optimization* Nonlinear Programming* Other Optimization Problems