Practical OptimizationNumerical optimization and parameter estimation are essential tools in a wide variety of applications, such as engineering, science, medicine, sociology and economics. For these optimization techniques to be exploited effectively, problem solvers need to be fully informed of the scope and organization of software for both the specialist and non-specialist; the underlying numerical methods; the aspects of problem formulation that affect performance; the assessment of computer results and the resolution of difficulties that may occur during the solution process. These topics form the basis of the organization of Practical Optimization. Much of the material about the estimation of results and the preparation of the problem has not been previously published. The book contains a description of methods for numerical optimization to a level which should make it a useful course text. It is intended that the book should be self-contained. Consequently, those elements of calculus, linear algebra and numerical analysis pertinent to optimization are reviewed in the opening chapters. This is the first book on optimization which discusses not only the methods but also the analysis of computed results and the preparation of problems before solution. |
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INTRODUCTION | 1 |
FUNDAMENTALS | 14 |
Notes and Selected Bibliography for Section 2 2 | 45 |
Copyright | |
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accuracy active set method approximation augmented Lagrangian barrier function bound Cholesky factorization columns computed condition number conjugate-gradient method consider constrained problem constrained subproblem corresponding defined deleted denote derivatives descent direction diagonal discussed in Section eigenvalues elements equality constraints equations error evaluations exact example feasible point finite-difference interval function values Gauss-Newton method Gill and Murray given gradient hence Hessian matrix indefinite inequality constraints iteration Lagrange multiplier estimates Lagrange multipliers Lagrangian Lagrangian function Lagrangian method least-squares problem linear combination linear constraints linear programming linear search linearly constrained minimum Newton method non-singular non-zero nonlinear constraints objective function orthogonal penalty function penalty parameter positive definite positive-definite problem functions procedure projected Hessian properties quadratic function quadratic program quasi-Newton method range-space rows satisfied scalar search direction sequence solution solve sparse steepest-descent step length strategy subspace techniques transformation unconstrained minimization univariate variables vector zero