Optimization by Vector Space MethodsEngineers 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. 
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Review: Optimization by Vector Space Methods
User Review  Carol M.  GoodreadsA gem of a book! Could have been named "Optimization in Finite and Infinite Dimensions, with Introduction to Functional Analysis." Even if you're not in Operations Research or controls, get this book ... Read full review
Review: Optimization by Vector Space Methods
User Review  GoodreadsA gem of a book! Could have been named "Optimization in Finite and Infinite Dimensions, with Introduction to Functional Analysis." Even if you're not in Operations Research or controls, get this book ... Read full review
Contents
INTRODUCTION  1 
LINEAR SPACES  11 
HILBERT SPACE  46 
APPROXIMATION  55 
OTHER MINIMUM NORM PROBLEMS  64 
LEASTSQUARES ESTIMATION  78 
DUAL SPACES  103 
EXTENSION FORM OF THE HAHNBANACH  110 
LINEAR OPERATORS AND ADJOINTS  143 
ADJOINTS  150 
OPTIMIZATION OF FUNCTIONALS  169 
GLOBAL THEORY OF CONSTRAINED OPTIMIZATION  213 
LOCAL THEORY OF CONSTRAINED OPTIMIZATION  239 
OPTIMAL CONTROL THEORY  254 
I0 ITERATIVE METHODS OF OPTIMIZATION  271 
GEOMETRIC FORM OF THE HAHNBANACH  129 
Common terms and phrases
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 corresponding defined definition denoted derivatives dimensional dual space element equal equivalent Example exists finite finitedimensional follows Frechet differentiable Gateaux differential geometric given gradient HahnBanach theorem hence Hilbert space inequality inner product interior point inverse Lagrange multiplier Lemma linear combination linear operator linear variety linear vector space linearly independent Lp spaces mapping matrix maximize minimum norm problems Newton's method nonlinear nonzero normal equations normed linear space normed space obtain optimal control optimization problems orthogonal orthonormal point x0 polynomial preHilbert space projection theorem Proof Proposition random variables random vector real numbers realvalued result satisfying scalar Section Show solution solved space H spave sphere subset Suppose technique theory transformation unique vector space zero