Numerical OptimizationSpringer Science & Business Media, 2006年6月6日 - 636 頁 This is a book for people interested in solving optimization problems. Because of the wide (and growing) use of optimization in science, engineering, economics, and industry, it is essential for students and practitioners alike to develop an understanding of optimization algorithms. Knowledge of the capabilities and limitations of these algorithms leads to a better understanding of their impact on various applications, and points the way to future research on improving and extending optimization algorithms and software. Our goal in this book is to give a comprehensive description of the most powerful, state-of-the-art, techniques for solving continuous optimization problems. By presenting the motivating ideas for each algorithm, we try to stimulate the reader’s intuition and make the technical details easier to follow. Formal mathematical requirements are kept to a minimum. Because of our focus on continuous problems, we have omitted discussion of important optimization topics such as discrete and stochastic optimization. |
內容
1 | |
11 | |
Line Search Methods 34 | 35 |
TrustRegion Methods | 65 |
Conjugate Gradient Methods | 101 |
Practical Newton Methods | 135 |
Calculating Derivatives | 165 |
QuasiNewton Methods | 193 |
NotesandReferences | 571 |
ImplicitFunctionTheorem | 583 |
GeometryofFeasibleSets | 584 |
OrderNotation | 589 |
RootFindingforScalarEquations | 590 |
ElementsofLinearAlgebra | 591 |
Norms | 592 |
Subspaces | 595 |
LargeScale QuasiNewton and Partially Separable Optimization | 223 |
Nonlinear LeastSquares Problems | 251 |
NotesandReferences | 273 |
Theory of Constrained Optimization | 314 |
NotesandReferences | 356 |
InteriorPoint Methods | 393 |
Exercises | 415 |
NotesandReferences | 436 |
Penalty Barrier and Augmented Lagrangian Methods 488 | 489 |
Sequential Quadratic Programming | 527 |
Eigenvalues Eigenvectors and the SingularValue Decomposition | 596 |
DeterminantandTrace | 597 |
CholeskyLUQR | 598 |
ShermanMorrisonWoodburyFormula | 603 |
ErrorAnalysisandFloatingPointArithmetic | 604 |
ConditioningandStability | 606 |
609 | |
622 | |
常見字詞
algorithm approach automatic differentiation BFGS BFGS method Bk+1 bound Cauchy point Chapter Cholesky choose columns components compute conjugate gradient method constrained optimization curvature decrease defined derivatives descent direction described diagonal differentiable discussion eigenvalues equality constraints equations evaluation example f(xk factorization feasible point formula function f global convergence Hessian approximation inequality constraints iteration Jacobian KKT conditions L-BFGS Lagrange multiplier Lagrangian LICQ line search linear program Lipschitz continuous matrix merit function minimizer Newton’s method nonlinear nonsingular nonzero norm objective function obtain optimization problems parameter partially separable positive definite primal–dual properties quadratic programming quasi-Newton methods require result satisfies scalar search direction second-order simplex solving SQP methods steepest descent step length strategy subproblem subspace sufficiently Suppose symmetric techniques term Theorem trust-region unconstrained update variables vector Wolfe conditions xk+1 zero