Optimization by Vector Space Methods
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.
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OTHER MINIMUM NORM PROBLEMS
EXTENSION FORM OF THE HAHNBANACH
LINEAR OPERATORS AND ADJOINTS
OPTIMIZATION OF FUNCTIONALS
GLOBAL THEORY OF CONSTRAINED OPTIMIZATION
LOCAL THEORY OF CONSTRAINED OPTIMIZATION
OPTIMAL CONTROL THEORY
I0 ITERATIVE METHODS OF OPTIMIZATION
GEOMETRIC FORM OF THE HAHNBANACH
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 finite-dimensional follows Frechet differentiable Gateaux differential geometric given gradient Hahn-Banach 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 pre-Hilbert space projection theorem Proof Proposition random variables random vector real numbers real-valued result satisfying scalar Section Show solution solved space H spave sphere subset Suppose technique theory transformation unique vector space zero