Optimization by Vector Space MethodsJohn Wiley & Sons, 23 de gen. 1997 - 352 pàgines Engineers must make decisions regarding the distribution of expensive resources in a manner that will be economically beneficial. This problem can be realistically formulated and logically analyzed with optimization theory. This book shows engineers how to use optimization theory to solve complex problems. Unifies the large field of optimization with a few geometric principles. Covers functional analysis with a minimum of mathematics. Contains problems that relate to the applications in the book. |
Continguts
INTRODUCTION | 1 |
The Main Principles | 8 |
2 | 14 |
NORMED LINEAR SPACES | 22 |
HILBERT SPACE | 46 |
APPROXIMATION | 55 |
Approximation and Fourier Series | 62 |
LEASTSQUARES ESTIMATION | 78 |
GEOMETRIC FORM OF THE HAHNBANACH | 129 |
LINEAR OPERATORS AND ADJOINTS | 143 |
ADJOINTS | 150 |
Duality Relations for Convex Cones | 157 |
OPTIMIZATION OF FUNCTIONALS | 169 |
GLOBAL THEORY OF CONSTRAINED OPTIMIZATION | 213 |
LOCAL THEORY OF CONSTRAINED OPTIMIZATION | 239 |
5 | 253 |
8 | 97 |
DUAL SPACES | 103 |
EXTENSION FORM OF THE HAHNBANACH | 110 |
7 | 116 |
ITERATIVE METHODS OF OPTIMIZATION | 271 |
METHODS FOR SOLVING CONSTRAINED | 297 |
| 321 | |
Altres edicions - Mostra-ho tot
Frases i termes més freqüents
adjoint applied arbitrary assume Banach space bounded linear functional Cauchy sequence chapter closed subspace components conjugate functional consider constraints contains continuous functions control problem convergence convex functional convex set definition denoted derivatives dimensional dual space element equivalent Example exists finite finite-dimensional follows Fréchet differentiable functional ƒ G(xo Gateaux differential geometric given gradient Hahn-Banach theorem hence Hilbert space hyperplane inequality inner product interior point inverse Lagrange multiplier Lemma linear combination linear operator linear variety linear vector space linearly independent mapping matrix minimum norm problems n-dimensional Newton's method nonzero normed linear space normed space optimal control optimization problems orthogonal orthonormal polynomial positive cone pre-Hilbert space projection theorem Proof Proposition random variables real numbers result satisfying scalar Section Show solution solved space H sphere subset subspace Suppose t₁ t₂ theory unique vector space x₁ y₁ zero