Numerical OptimizationSpringer Science & Business Media, 2000年4月28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
Fundamentals of Unconstrained Optimization | 11 |
InteriorPoint Methods | 14 |
3 | 30 |
4 | 55 |
Notes and References | 61 |
3 | 87 |
Conjugate Gradient Methods | 102 |
Notes and References | 124 |
Notes and References | 356 |
5 | 374 |
Pricing and Selection of the Entering Index | 381 |
2 | 401 |
3 | 407 |
Notes and References | 414 |
Notes and References | 436 |
6 | 474 |
3 | 142 |
Gershgorin Modification | 150 |
Calculating Derivatives | 162 |
Vector Functions and Partial Separability | 183 |
Notes and References | 189 |
Properties of SR1 Updating | 205 |
4 | 211 |
Notes and References | 219 |
Algorithms for Partially Separable Functions | 244 |
Nonlinear LeastSquares Problems | 251 |
Notes and References | 310 |
2 | 319 |
3 | 331 |
Notes and References | 483 |
Algorithmic Framework | 492 |
3 | 510 |
Sequential Quadratic Programming | 528 |
9 | 558 |
A Background Material | 576 |
A 1 | 582 |
References | 609 |
620 | |
622 | |
632 | |
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常見字詞
algorithm approach approximate solution automatic differentiation BFGS BFGS method Bk+1 bound Cauchy point Chapter Cholesky factorization choose columns components compute conjugate gradient method constrained optimization curvature decrease defined derivatives descent direction described diagonal discussed eigenvalues elements evaluation example feasible point feasible sequence Figure function f global convergence Hessian approximation implementation inequality constraints Jacobian KKT conditions L-BFGS Lagrange multiplier Lagrangian Lemma LICQ line search linear programming Lipschitz continuous matrix merit function minimizer Newton step Newton's method node nonsingular nonzero norm objective function obtain optimization problems parameter partially separable positive definite proof properties quadratic programming quasi-Newton methods region require result satisfies scalar search direction second-order solving steepest descent step length strategy subproblem subspace sufficiently Suppose symmetric techniques Theorem trust-region unconstrained V² ƒ variables vector Wolfe conditions xk+1 zero