A01=Lucien W. Neustadt
Absolute continuity
Adjoint equation
Affine space
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Associative property
Author_Lucien W. Neustadt
automatic-update
Banach space
Boundary value problem
Bounded variation
Category1=Non-Fiction
Category=PB
Category=PBU
Category=TB
Cauchy sequence
Chain rule
Characterization (mathematics)
Compact space
Continuous function (set theory)
Control function (econometrics)
Convex combination
Convex cone
Convex set
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Differentiable function
Differential equation
Dimension (vector space)
Direct product
eq_bestseller
eq_isMigrated=2
eq_nobargain
eq_non-fiction
eq_tech-engineering
Equation
Euclidean topology
Existential quantification
Finite difference
Fréchet derivative
Function problem
Fundamental lemma (Langlands program)
General position
Hamiltonian mechanics
I0
Identity matrix
Integral equation
Jacobian matrix and determinant
Lagrange multiplier
Language_English
Lebesgue measure
Limit point
Linear differential equation
Linear map
Linear subspace
Linearization
Mathematical optimization
Maximum principle
Measurable function
N-vector
Norm (mathematics)
Open set
Operator (physics)
Optimal control
Optimization problem
Order of integration (calculus)
Ordinary differential equation
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Parameter
Pointwise
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Quasiconvex function
Requirement
Set (mathematics)
Sign (mathematics)
Simultaneous equations
softlaunch
Special case
Subderivative
Subsequence
Subset
Theorem
Topological space
Uniform continuity
Vector space
Volterra integral equation
Volterra operator
Weierstrass M-test
Without loss of generality
Product details
- ISBN 9780691616834
- Weight: 595g
- Dimensions: 152 x 235mm
- Publication Date: 08 Mar 2015
- Publisher: Princeton University Press
- Publication City/Country: US
- Product Form: Paperback
- Language: English
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This book presents a comprehensive treatment of necessary conditions for general optimization problems. The presentation is carried out in the context of a general theory for extremal problems in a topological vector space setting. Following a brief summary of the required background, generalized Lagrange multiplier rules are derived for optimization problems with equality and generalized "inequality" constraints. The treatment stresses the importance of the choice of the underlying set over which the optimization is to be performed, the delicate balance between differentiability-continuity requirements on the constraint functionals, and the manner in which the underlying set is approximated by a convex set. The generalized multiplier rules are used to derive abstract maximum principles for classes of optimization problems defined in terms of operator equations in a Banach space. It is shown that special cases include the usual maximum principles for general optimal control problems described in terms of diverse systems such as ordinary differential equations, functional differential equations, Volterra integral equations, and difference equations.
Careful distinction is made throughout the analysis between "local" and "global" maximum principles. Originally published in 1977. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.
