Topics in optimization / edited by George Leitmann.

Format:

Book

Contributor:

Leitmann, George, editor.

Series:

Mathematics in science and engineering

Language:

English

Subjects (All):

Mathematical optimization.

Control theory.

Physical Description:

1 online resource (487 p.)

Place of Publication:

New York, New York ; London, England : Academic Press, 1967.

Language Note:

English

Summary:

Topics in optimization

Contents:

Front Cover; TOPICS IN OPTIMIZATION; Copyright Page; Contents; List of Contributors; Preface; Part 1 A Variational Approach; Chapter 1. Inequalities in a Variational Problem; 1.0 Introduction; 1.1 Condition I; 1.2 Conditions II and III; PART A-CASE (a); 1.3 Preliminary Considerations; 1.4 Singularities in Case (a); 1.5 The Extremaloid Index; 1.6 The Imbedding Construction; 1.7 Condition IV; 1.8 Proof of Sufficiency; 1.9 Numerical Example; PART B-CASE (b); 1.10 Preliminary Considerations; 1.11 Singularities in Case (b); 1.12 The Imbedding Construction; 1.13 Numerical Example

1.14 Discussion of the ResultsReferences; Chapter 2. Discontinuities in a Variational Problem; 2.0 Introduction; 2.1 Conditions Ic and Id; PART A-CASE (a); 2.2 Conditions la, Ib, II, and III; 2.3 Preliminary Considerations; 2.4 The Function h(y'); 2.5 Zermelo Diagram; 2.6 The Imbedding Construction; 2.7 Condition IV'; 2.8 The Hilbert Integral; 2.9 Proof of Sufficiency; 2.10 Numerical Example; 2.11 Discussion of the Results; PART B-CASE (b); 2.12 Conditions Ia, Ib, II, and III; 2.13 Preliminary Considerations; 2.14 Zermelo Diagram; 2.15 Corner Manifolds; 2.16 Conditions II' and IIN'

2.17 Free Corners2.18 A Special Case; 2.19 The Imbedding Construction; 2.20 Proof of Sufficiency; 2.21 Numerical Example; 2.22 Discussion of the Results; References; Chapter 3. Singular Extremals; 3.0 Introduction; 3.1 Second Variation Test for Singular Extremals; 3.2 A Transformation Approach to the Analysis of Singular Subarcs; 3.3 Examples; References; Chapter 4. Thrust Programming in a Central Gravitational Field; 4.1 General Equations Governing the Motion of a Boosting Vehicle in a Central Gravitational Field; 4.2 Integrals of the Basic System of Equations

4.3 Boundary Conditions: Various Types of Motion4.4 Orbits on a Spherical Surface; 4.5 Boosting Devices of Limited Propulsive Power; 4.6 Singular Control Regimes; References; Chapter 5. The Mayer-Bolza Problem for Multiple Integrals: Some Optimum Problems for Elliptic Differential Equations Arising in Magnetohydrodynamics; 5.0 Introduction; 5.1 Optimum Problems for Partial Differential Equations: Necessary Conditions of Optimality; 5.2 Optimum Problems in the Theory of Magnetohydrodynamical Channel Flow

5.3 Application to the Theory of MHD Power Generation: Minimization ofEnd Effects in an MHD ChannelAppendix; References; Part 2 A Geometric Approach; Chapter 6. Mathematical Foundations of System Optimization; 6.0 Introduction; 6.1 Dynamical Polysystem; 6.2 Optimization Problem; 6.3 The Principle of Optimal Evolution; 6.4 Statement of the Maximum Principle; 6.5 Proof of the Maximum Principle for an Elementary Dynamical Polysystem; 6.6 Proof of the Maximum Principle for a Linear Dynamical Polysystem; 6.7 Proof of the Maximum Principle for a General Dynamical Polysystem

6.8 Uniformly Continuous Dependence of Trajectories with Respect to Variations of the Control Functions

Notes:

Includes indexes.

Description based on print version record.

ISBN:

1-282-76980-4

9786612769801

0-08-095538-X

OCLC:

699474070