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1.

図書
図書
1. Infinite dimensional optimization and control theory (: pbk)
H.O. Fattorini
出版情報: Cambridge : Cambridge University Press, 1999  xv, 798 p. ; 25 cm
シリーズ名: Encyclopedia of mathematics and its applications / edited by G.-C. Rota ; v. 62
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Finite Dimensional Control Problems / Part I：
Calculus of variations and control theory / 1：
Optimal control problems without target conditions / 2：
Abstract minimization problems: the minimum principle for the time optimal problem / 3：
Abstract minimization problems: the minimum principle for general optimal control problems / 4：
Infinite Dimensional Control Problems / Part II：
Differential equations in Banach spaces and semigroup theory / 5：
Abstract minimization problems in Hilbert spaces: applications to hyperbolic control systems / 6：
Abstract minimization problems in Banach spaces: abstract parabolic linear and semilinear equations / 7：
Interpolation and domains of fractional powers / 8：
Linear control systems / 9：
Optimal control problems with state constraints / 10：
Optimal control problems with state constraints: The abstract parabolic case / 11：
Relaxed Controls / Part III：
Spaces of relaxed controls: topology and measure theory / 12：
Relaxed controls in finite dimensional systems: existence theory / 13：
Relaxed controls in infinite dimensional spaces: existence theory / 14：
Finite Dimensional Control Problems / Part I：
Calculus of variations and control theory / 1：
Optimal control problems without target conditions / 2：
2.

図書
図書
2. Calculus of variations and optimal control
A.A. Milyutin, N.P. Osmolovskii
出版情報: Providence, R.I. : American Mathematical Society, c1998  xii, 372 p. ; 27 cm
シリーズ名: Translations of mathematical monographs ; v. 180
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First order conditions: First order conditions
Theory of a weak minimum for the problem on a fixed time interval
Theory of the maximum principle
Extremals and the Hamiltonian of a control system
Hamilton-Jacobi equation and field theory
Transformations of problems and invariance of extremals
Quadratic conditions: Quadratic conditions and conjugate points for broken extremals
Quadratic conditions for a Pontryagin minimum and sufficient conditions for a strong minimum: Proofs
Quadratic conditions in the general problem of the calculus of variations and related optimal control problems
Investigation of extremals by quadratic conditions: Examples
Bibliography
First order conditions: First order conditions
Theory of a weak minimum for the problem on a fixed time interval
Theory of the maximum principle
3.

図書
図書
3. Relaxation in optimization theory and variational calculus
Tomáš Roubiček
出版情報: Berlin ; New York : Walter de Gruyter, 1997  xiv, 474 p. ; 25 cm
シリーズ名: De Gruyter series in nonlinear analysis and applications ; 4
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4.

図書
図書
4. Recent developments in well-posed variational problems
edited by Roberto Lucchetti and Julian Revalski
出版情報: Dordrecht ; Boston : Kluwer Academic Publishers, c1995  viii, 266 p. ; 25 cm
シリーズ名: Mathematics and its applications ; v. 331
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5.

図書
図書
5. Stories about maxima and minima
V.M. Tikhomirov ; translated from the Russian by Abe Shenitzer
出版情報: Providence, R.I. : American Mathematical Society, c1990  xi, 187 p. ; 26 cm
シリーズ名: Mathematical world ; v. 1
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Ancient maximum and minimum problems / Part 1：
Why do we solve maximum and minimum problems?
The oldest problem-Dido's problem Maxima and minima in nature ( optics$)$
Maxima and minima in geometry
Maxima and minima in algebra and in analysis Kepler's problem
The brachistochrone Newton's aerodynamical problem
Methods of solution of extremal problems / Part 2：
What is a function?
What is an extremal problem?
Extrema of functions of one variable
Extrema of functions of many variables
Lagrange's principle More problem solving
What happened later in the theory of extremal problems?
More accurately, a discussion
Ancient maximum and minimum problems / Part 1：
Why do we solve maximum and minimum problems?
The oldest problem-Dido's problem Maxima and minima in nature ( optics$)$
6.

図書
図書
6. Dynamic optimization : the calculus of variations and optimal control in economics and management. 2nd ed
Morton I. Kamien and Nancy L. Schwartz
出版情報: Amsterdam ; Tokyo : North-Holland , New York, N.Y. : Elsevier Science [distributors outside the United States and Canada], c1991  xvii, 377 p. ; 24 cm
シリーズ名: Advanced textbooks in economics ; v. 31
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Preface to the Fourth Printing
Preface to the Second Edition
Preface to the First Edition
Calculus of Variations / Part I：
Introduction / Section 1：
Example Solved / Section 2：
Simplest Problem-Euler Equation / Section 3：
Examples and Interpretations / Section 4：
Solving the Euler Equation in Special Cases / Section 5：
Second Order Conditions / Section 6：
Isoperimetric Problem / Section 7：
Free End Value / Section 8：
Free Horizon-Transversality Conditions / Section 9：
Equality Constrained Endpoint / Section 10：
Salvage Value / Section 11：
Inequality Constraint Endpoints and Sensitivity Analysis / Section 12：
Corners / Section 13：
Inequality Constraints in (t, x) / Section 14：
Infinite Horizon Autonomous Problems / Section 15：
Most Rapid Approach Paths / Section 16：
Diagrammatic Analysis / Section 17：
Several Functions and Double Integrals / Section 18：
Optimal Control / Part II：
Simplest Problem-Necessary Conditions
Sufficiency
Interpretations
Several Variables
Fixed Endpoint Problems
Various Endpoint Conditions
Discounting, Current Values, Comparative Dynamics
Equilibria in Infinite Horizon Autonomous Problems
Bounded Controls
Further Control Constraint
Discontinuous and Bang-Bang Control
Singular Solutions and Most Rapid Approach Paths
The Pontryagin Maximum Principle, Existence
Further Sufficiency Theorems
Alternative Formulations
State Variable Inequality Constraints
Jumps in the State Variable, Switches in State Equations
Delayed Response / Section 19：
Optimal Control with Integral State Equations / Section 20：
Dynamic Programming / Section 21：
Stochastic Optimal Control / Section 22：
Differential Games / Section 23：
Calculus and Nonlinear Programming / Appendix A：
Calculus Techniques
Mean-Value Theorems
Concave and Convex Functions
Maxima and Minima
Equality Constrained Optimization
Inequality Constrained Optimization
Line Integrals and Green's Theorem
Differential Equations / Appendix B：
Linear First Order Differential Equations
Linear Second Order Differential Equations
Linear nth Order Differential Equations
A Pair of Linear Equations
Existence and Uniqueness of Solutions
References
Author Index
Subject Index
Preface to the Fourth Printing
Preface to the Second Edition
Preface to the First Edition
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