Variational Calculus and Optimal Control: Optimization with Elementary Convexity (Undergraduate Texts in Mathematics) - hardcover
1995, ISBN: 9780387945118
Springer, Gebundene Ausgabe, Auflage: 2nd ed. 1996, 477 Seiten, Publiziert: 1995-12-01T00:00:01Z, Produktgruppe: Buch, 4.14 kg, Verkaufsrang: 2314086, Analysis, Naturwissenschaft & Mathem… More...
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Variational Calculus and Optimal Control: Optimization with Elementary Convexity (Undergraduate Texts in Mathematics) - hardcover
1995, ISBN: 9780387945118
Springer, Gebundene Ausgabe, Auflage: 2nd ed. 1996, 477 Seiten, Publiziert: 1995-12-01T00:00:01Z, Produktgruppe: Buch, 4.14 kg, Verkaufsrang: 2314086, Analysis, Naturwissenschaft & Mathem… More...
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Variational Calculus and Optimal Control: Optimization with Elementary Convexity (Undergraduate Texts in Mathematics) - hardcover
1995, ISBN: 9780387945118
Springer, Gebundene Ausgabe, Auflage: 2nd ed. 1996, 477 Seiten, Publiziert: 1995-12-01T00:00:01Z, Produktgruppe: Buch, 1.88 kg, Verkaufsrang: 1653247, Analysis, Naturwissenschaft & Mathem… More...
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Variational Calculus and Optimal Control: Optimization with Elementary Convexity (Undergraduate Texts in Mathematics) - hardcover
1995, ISBN: 9780387945118
Springer, Gebundene Ausgabe, Auflage: 2nd ed. 1996, 477 Seiten, Publiziert: 1995-12-01T00:00:01Z, Produktgruppe: Buch, 1.88 kg, Verkaufsrang: 1653247, Analysis, Naturwissenschaft & Mathem… More...
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Variational Calculus and Optimal Control: Optimization with Elementary Convexity (Undergraduate Texts in Mathematics) - hardcover
1995, ISBN: 0387945113
[EAN: 9780387945118], Gebraucht, guter Zustand, [SC: 4.03], [PU: Springer], TROUTMAN JOHN L. VARIATIONAL CALCULUS AND OPTIMAL CONTROL OPTIMIZATION WITH ELEMENTARY CONVEXITY UNDERGRADUATE … More...
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Variational Calculus and Optimal Control: Optimization with Elementary Convexity (Undergraduate Texts in Mathematics) - hardcover
1995, ISBN: 9780387945118
Springer, Gebundene Ausgabe, Auflage: 2nd ed. 1996, 477 Seiten, Publiziert: 1995-12-01T00:00:01Z, Produktgruppe: Buch, 4.14 kg, Verkaufsrang: 2314086, Analysis, Naturwissenschaft & Mathem… More...
Troutman, John L.:
Variational Calculus and Optimal Control: Optimization with Elementary Convexity (Undergraduate Texts in Mathematics) - hardcover1995, ISBN: 9780387945118
Springer, Gebundene Ausgabe, Auflage: 2nd ed. 1996, 477 Seiten, Publiziert: 1995-12-01T00:00:01Z, Produktgruppe: Buch, 4.14 kg, Verkaufsrang: 2314086, Analysis, Naturwissenschaft & Mathem… More...
Variational Calculus and Optimal Control: Optimization with Elementary Convexity (Undergraduate Texts in Mathematics) - hardcover
1995
ISBN: 9780387945118
Springer, Gebundene Ausgabe, Auflage: 2nd ed. 1996, 477 Seiten, Publiziert: 1995-12-01T00:00:01Z, Produktgruppe: Buch, 1.88 kg, Verkaufsrang: 1653247, Analysis, Naturwissenschaft & Mathem… More...
Variational Calculus and Optimal Control: Optimization with Elementary Convexity (Undergraduate Texts in Mathematics) - hardcover
1995, ISBN: 9780387945118
Springer, Gebundene Ausgabe, Auflage: 2nd ed. 1996, 477 Seiten, Publiziert: 1995-12-01T00:00:01Z, Produktgruppe: Buch, 1.88 kg, Verkaufsrang: 1653247, Analysis, Naturwissenschaft & Mathem… More...
Variational Calculus and Optimal Control: Optimization with Elementary Convexity (Undergraduate Texts in Mathematics) - hardcover
1995, ISBN: 0387945113
[EAN: 9780387945118], Gebraucht, guter Zustand, [SC: 4.03], [PU: Springer], TROUTMAN JOHN L. VARIATIONAL CALCULUS AND OPTIMAL CONTROL OPTIMIZATION WITH ELEMENTARY CONVEXITY UNDERGRADUATE … More...
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Details of the book - Variational Calculus and Optimal Control: Optimization with Elementary Convexity (Undergraduate Texts in Mathematics)
EAN (ISBN-13): 9780387945118
ISBN (ISBN-10): 0387945113
Hardcover
Publishing year: 2007
Publisher: Springer
482 Pages
Weight: 0,906 kg
Language: eng/Englisch
Book in our database since 2007-06-12T09:39:47+01:00 (London)
Detail page last modified on 2023-11-05T07:53:54+00:00 (London)
ISBN/EAN: 9780387945118
ISBN - alternate spelling:
0-387-94511-3, 978-0-387-94511-8
Alternate spelling and related search-keywords:
Book author: john troutman, lagrange, bernoulli
Book title: optimization optimal control, calculus elementary, variational calculus optimal control, convexity, convex optimization, and, john
Information from Publisher
Author: John L. Troutman
Title: Undergraduate Texts in Mathematics; Variational Calculus and Optimal Control - Optimization with Elementary Convexity
Publisher: Springer; Springer US
462 Pages
Publishing year: 1995-12-01
New York; NY; US
Weight: 1,880 kg
Language: English
85,59 € (DE)
87,99 € (AT)
94,50 CHF (CH)
POD
XV, 462 p.
BB; Calculus of Variations and Optimal Control; Optimization; Hardcover, Softcover / Mathematik/Sonstiges; Optimierung; Verstehen; Calculus; Convexity; Konvexe Funktion; Optimal control; Variationsrechnung; linear optimization; optimization; Systems Theory, Control; Calculus of Variations and Optimization; Systems Theory, Control; Kybernetik und Systemtheorie; BB; BC; EA
0 Review of Optimization in ?d.- Problems.- One Basic Theory.- 1 Standard Optimization Problems.- 1.1. Geodesic Problems.- (a) Geodesics in ?d.- (b) Geodesics on a Sphere.- (c) Other Geodesic Problems.- 1.2. Time-of-Transit Problems.- (a) The Brachistochrone.- (b) Steering and Control Problems.- 1.3. Isoperimetric Problems.- 1.4. Surface Area Problems.- (a) Minimal Surface of Revolution.- (b) Minimal Area Problem.- (c) Plateau’s Problem.- 1.5. Summary: Plan of the Text.- Notation: Uses and Abuses.- Problems.- 2 Linear Spaces and Gâteaux Variations.- 2.1. Real Linear Spaces.- 2.2. Functions from Linear Spaces.- 2.3. Fundamentals of Optimization.- Constraints.- Rotating Fluid Column.- 2.4. The Gâteaux Variations.- Problems.- 3 Minimization of Convex Functions.- 3.1. Convex Functions.- 3.2. Convex Integral Functions.- Free End-Point Problems.- 3.3. [Strongly] Convex Functions.- 3.4. Applications.- (a) Geodesics on a Cylinder.- (b) A Brachistochrone.- (c) A Profile of Minimum Drag.- (d) An Economics Problem.- (e) Minimal Area Problem.- 3.5. Minimization with Convex Constraints.- The Hanging Cable.- Optimal Performance.- 3.6. Summary: Minimizing Procedures.- Problems.- 4 The Lemmas of Lagrange and Du Bois-Reymond.- Problems.- 5 Local Extrema in Normed Linear Spaces.- 5.1. Norms for Linear Spaces.- 5.2. Normed Linear Spaces: Convergence and Compactness.- 5.3. Continuity.- 5.4. (Local) Extremal Points.- 5.5. Necessary Conditions: Admissible Directions.- 5.6*. Affine Approximation: The Fréchet Derivative.- Tangency.- 5.7. Extrema with Constraints: Lagrangian Multipliers.- Problems.- 6 The Euler-Lagrange Equations.- 6.1. The First Equation: Stationary Functions.- 6.2. Special Cases of the First Equation.- (a) When f = f(z).- (b) When f = f(x,z).- (c) When f = f(y,z).- 6.3. The Second Equation.- 6.4. Variable End Point Problems: Natural Boundary Conditions.- Jakob Bernoulli’s Brachistochrone.- Transversal Conditions*.- 6.5. Integral Constraints: Lagrangian Multipliers.- 6.6. Integrals Involving Higher Derivatives.- Buckling of a Column under Compressive Load.- 6.7. Vector Valued Stationary Functions.- The Isoperimetric Problem.- Lagrangian Constraints*.- Geodesics on a Surface.- 6.8*. Invariance of Stationarity.- 6.9. Multidimensional Integrals.- Minimal Area Problem.- Natural Boundary Conditions.- Problems.- Two Advanced Topics.- 7 Piecewise C1 Extremal Functions.- 7.1. Piecewise C1 Functions.- (a) Smoothing.- (b) Norms for ?1.- 7.2. Integral Functions on ?1.- 7.3. Extremals in ?1 [a, b]: The Weierstrass-Erdmann Corner Conditions.- A Sturm-Liouville Problem.- 7.4. Minimization Through Convexity.- Internal Constraints.- 7.5. Piecewise C1 Vector-Valued Extremals.- Minimal Surface of Revolution.- Hilbert’s Differentiability Criterion*.- 7.6*. Conditions Necessary for a Local Minimum.- (a) The Weierstrass Condition.- (b) The Legendre Condition.- Bolza’s Problem.- Problems.- 8 Variational Principles in Mechanics.- 8.1. The Action Integral.- 8.2. Hamilton’s Principle: Generalized Coordinates.- Bernoulli’s Principle of Static Equilibrium.- 8.3. The Total Energy.- Spring-Mass-Pendulum System.- 8.4. The Canonical Equations.- 8.5. Integrals of Motion in Special Cases.- Jacobi’s Principle of Least Action.- Symmetry and Invariance.- 8.6. Parametric Equations of Motion.7*. The Hamilton-Jacobi Equation.- 8.8. Saddle Functions and Convexity; Complementary Inequalities.- The Cycloid Is the Brachistochrone.- Dido’s Problem.- 8.9. Continuous Media.- (a) Taut String.- The Nonuniform String.- (b) Stretched Membrane.- Static Equilibrium of (Nonplanar) Membrane.- Problems.- 9 Sufficient Conditions for a Minimum.- 9.1. The Weierstrass Method.- 9.2. [Strict] Convexity of f(x,Y, Z).- 9.3. Fields.- Exact Fields and the Hamilton-Jacobi Equation*.- 9.4. Hilbert’s Invariant Integral.- The Brachistochrone*.- Variable End-Point Problems.- 9.5. Minimization with Constraints.- The Wirtinger Inequality.- 9.6*. Central Fields.- Smooth Minimal Surface of Revolution.- 9.7. Construction of Central Fields with Given Trajectory: The Jacobi Condition.- 9.8. Sufficient Conditions for a Local Minimum.- (a) Pointwise Results.- Hamilton’s Principle.- (b) Trajectory Results.- 9.9*. Necessity of the Jacobi Condition.- 9.10. Concluding Remarks.- Problems.- Three Optimal Control.- 10 Control Problems and Sufficiency Considerations.- 10.1. Mathematical Formulation and Terminology.- 10.2. Sample Problems.- (a) Some Easy Problems.- (b) A Bolza Problem.- (c) Optimal Time of Transit.- (d) A Rocket Propulsion Problem.- (e) A Resource Allocation Problem.- (f) Excitation of an Oscillator.- (g) Time-Optimal Solution by Steepest Descent.- 10.3. Sufficient Conditions Through Convexity.- Linear State-Quadratic Performance Problem.- 10.4. Separate Convexity and the Minimum Principle.- Problems.- 11 Necessary Conditions for Optimality.- 11.1. Necessity of the Minimum Principle.- (a) Effects of Control Variations.- (b) Autonomous Fixed Interval Problems.- Oscillator Energy Problem.- (c) General Control Problems.- 11.2. Linear Time-Optimal Problems.- Problem Statement.- A Free Space Docking Problem.- 11.3. General Lagrangian Constraints.- (a) Control Sets Described by Lagrangian Inequalities.- (b)* Variational Problems with Lagrangian Constraints.- (c) Extensions.- Problems.- A.1. The Intermediate and Mean Value Theorems.- A.2. The Fundamental Theorem of Calculus.- A.3. Partial Integrals: Leibniz’ Formula.- A.4. An Open Mapping Theorem.- A.5. Families of Solutions to a System of Differential Equations.- A.6. The Rayleigh Ratio.- Historical References.- Answers to Selected Problems.More/other books that might be very similar to this book
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