Optimization (eBook)

A Theory of Necessary Conditions

Lucien W. Neustadt (Autor)

eBook Download: PDF

2015
Princeton University Press (Verlag)
978-1-4008-7053-0 (ISBN)

Infos

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.

Produkt-Details

• Erscheint lt. Verlag: 8.3.2015
• Reihe/Serie: Princeton Legacy Library
• Reihe/Serie: Princeton Legacy Library
• Verlagsort: Princeton
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Mathematik
• Themenwelt: Technik
• Schlagworte: absolute continuity • Abuse of notation • adjoint equation • Affine space • associative property • Banach space • Barycentric coordinate system • Boundary (topology) • Boundary value problem • Bounded Variation • Cauchy Sequence • chain rule • Characterization (mathematics) • Codomain • Compact space • Continuous function (set theory) • Control function (econometrics) • Convex body • convex combination • Convex cone • convex set • counterexample • Derivative • Differentiable function • Differential Calculus • differential equation • Dimension (vector space) • direct product • Equation • Euclidean space • Euclidean topology • existential quantification • Finite difference • Fréchet derivative • Fritz John • Function problem • Fundamental lemma (Langlands program) • General position • hamiltonian mechanics • Homeomorphism • hyperplane • I0 • Identity matrix • Initial Condition • integral equation • Interior (topology) • Jacobian matrix and determinant • Lagrange multiplier • Lebesgue measure • Limit point • linear differential equation • Linear Function • Linearization • Linear map • Linear subspace • Locally convex topological vector space • Mathematical Optimization • Maximum principle • Measurable function • Measure (mathematics) • multiple Integral • Natural number • Norm (mathematics) • N-vector • Open set • Operator (physics) • optimal control • optimization problem • Order of integration (calculus) • ordinary differential equation • Parameter • Phase space • Pointwise • Quasiconvex function • representation theorem • Requirement • scalar multiplication • scientific notation • Set (mathematics) • Sign (mathematics) • Simultaneous Equations • Smoothness • space form • Special case • state variable • step function • Subderivative • subsequence • Subset • Summation • Theorem • Topological space • topological vector space • uniform continuity • uniform convergence • Vector Space • Volterra integral equation • Volterra operator • Weierstrass M-test • Without loss of generality
• ISBN-10: 1-4008-7053-4 / 1400870534
• ISBN-13: 978-1-4008-7053-0 / 9781400870530