Optimization By Vector Space Methods 9780471181170 2025 pdf kindle mobi epub 下载 百度云盘

　　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.

Linear Spaces.

Hilbert Space.

Least-Squares Estimation.

Dual Spaces.

Linear Operators and Adjoints.

Optimization of Functionals.

Global Theory of Constrained Optimization.

Local Theory of Constrained Optimization.

Iterative Methods of Optimization.

Indexes.

　　DAVID G. LUENBERGER is a professor in the School of

Engineering at Stanford University. He has published four textbooks

and over 70 technical papers. Professor Luenberger is a Fellow of

the Institute of Electrical and Electronics Engineers and recipient

of the 1990 Bode Lecture Award. His current research is mainly in

investment science, economics, and planning.

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Proposition 1. Let X be a Banach space, M a closed subspace of X, and X/M the quotient space with the quotient norm defined as above. Then X/M is also a Banach space.

Since the solution to the approximation problem is equivalent to solution to the normal equations, it is clear that the Gram-Schmidt procedure can be interpreted as a procedure for inverting the Gram matrix. Conversely, many effective algorithms for solving the normal equations have an interpretation in terms of the minimum norm problem in Hilbert space. (p. 63)

书籍介绍

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.