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1.

図書

図書
James Renegar
出版情報: Philadelphia, PA : SIAM , Philadelphia, PA : MPS, 2001  vii, 117 p. ; 26 cm
シリーズ名: MPS-SIAM series on optimization
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Preface
Preliminaries / 1:
Linear Algebra / 1.1:
Gradients / 1.2:
Hessians / 1.3:
Convexity / 1.4:
Fundamental Theorems of Calculus / 1.5:
Newton's Method / 1.6:
Basic Interior-Point Method Theory / 2:
Intrinsic Inner Products / 2.1:
Self-Concordant Functionals / 2.2:
Introduction / 2.2.1:
Self-Concordancy and Newton's Method / 2.2.2:
Other Properties / 2.2.3:
Barrier Functionals / 2.3:
Analytic Centers / 2.3.1:
Optimal Barrier Functionals / 2.3.3:
Logarithmic Homogeneity / 2.3.4:
Primal Algorithms / 2.4:
The Barrier Method / 2.4.1:
The Long-Step Barrier Method / 2.4.3:
A Predictor-Corrector Method / 2.4.4:
Matters of Definition / 2.5:
Conic Programming and Duality / 3:
Conic Programming / 3.1:
Classical Duality Theory / 3.2:
The Conjugate Functional / 3.3:
Duality of the Central Paths / 3.4:
Self-Scaled (or Symmetric) Cones / 3.5:
An Important Remark on Notation / 3.5.1:
Scaling Points / 3.5.3:
Gradients and Norms / 3.5.4:
A Useful Theorem / 3.5.5:
The Nesterov--Todd Directions / 3.6:
Primal-Dual Path-Following Methods / 3.7:
Measures of Proximity / 3.7.1:
An Algorithm / 3.7.2:
Another Algorithm / 3.7.3:
A Primal-Dual Potential-Reduction Method / 3.8:
The Potential Function / 3.8.1:
The Algorithm / 3.8.2:
The Analysis / 3.8.3:
Bibliography
Index
Preface
Preliminaries / 1:
Linear Algebra / 1.1:
2.

図書

図書
Michael D. Intriligator
出版情報: Philadelphia, Pa : Society for Industrial and Applied Mathematics, c2002  xix, 508 p. ; 23 cm
シリーズ名: Classics in applied mathematics ; 39
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Preface to the Classics Edition
Preface
Introduction / Part 1:
Economizing and the Economy / 1:
The Economizing Problem / 1.1:
Institutions of the Economy / 1.2:
Economics / 1.3:
Static Optimization / Part 2:
The Mathematical Programming Problem / 2:
Formal Statement of the Problem / 2.1:
Types of Maxima, the Weierstrass Theorem, and the Local-Global Theorem / 2.2:
Geometry of the Problem / 2.3:
Classical Programming / 3:
The Unconstrained Case / 3.1:
The Method of Lagrange Multipliers / 3.2:
The Interpretation of the Lagrange Multipliers / 3.3:
Problems
Nonlinear Programming / 4:
The Case of No Inequality Constraints / 4.1:
The Kuhn-Tucker Conditions / 4.2:
The Kuhn-Tucker Theorem / 4.3:
Solution Algorithms / 4.4:
Linear Programming / 5:
The Dual Problems of Linear Programming / 5.1:
The Lagrangian Approach; Existence, Duality and Complementary Slackness Theorems / 5.2:
The Interpretation of the Dual / 5.3:
The Simplex Algorithm / 5.4:
Game Theory / 6:
Classification and Description of Games / 6.1:
Two-person, Zero-sum Games / 6.2:
Two-person Nonzero-sum Games / 6.3:
Cooperative Games / 6.4:
Games With Infinitely Many Players / 6.5:
Applications of Static Optimization / Part 3:
Theory of the Household / 7:
Commodity Space / 7.1:
The Preference Relation / 7.2:
The Neoclassical Problem of the Household / 7.3:
Comparative Statics of the Household / 7.4:
Revealed Preference / 7.5:
von Neumann-Morgenstern Utility / 7.6:
Theory of the Firm / 8:
The Production Function / 8.1:
The Neoclassical Theory of the Firm / 8.2:
Comparative Statics of the Firm / 8.3:
Imperfect Competition: Monopoly and Monopsony / 8.4:
Competition Among the Few: Oligopoly and Oligopsony / 8.5:
General Equilibrium / 9:
The Classical Approach: Counting Equations and Unknowns / 9.1:
The Input-Output Linear Programming Approach / 9.2:
The Neoclassical Excess Demand Approach / 9.3:
Stability of Equilibrium / 9.4:
The von Neumann Model of an Expanding Economy / 9.5:
Welfare Economics / 10:
The Geometry of the Problem in the 2 x 2 x 2 Case / 10.1:
Competitive Equilibrium and Pareto Optimality / 10.2:
Market Failure / 10.3:
Optimality Over Time / 10.4:
Dynamic Optimization / Part 4:
The Control Problem / 11:
Some Special Cases / 11.1:
Types of Control / 11.3:
The Control Problem as One of Programming in an Infinite Dimensional Space; the Generalized Weierstrass Theorem / 11.4:
Calculus of Variations / 12:
Euler Equation / 12.1:
Necessary Conditions / 12.2:
Transversality Condition / 12.3:
Constraints / 12.4:
Dynamic Programming / 13:
The Principle of Optimality and Bellman's Equation / 13.1:
Dynamic Programming and the Calculus of Variations / 13.2:
Dynamic Programming Solution of Multistage Optimization Problems / 13.3:
Maximum Principle / 14:
Costate Variables, the Hamiltonian, and the Maximum Principle / 14.1:
The Interpretation of the Costate Variables / 14.2:
The Maximum Principle and the Calculus of Variations / 14.3:
The Maximum Principle and Dynamic Programming / 14.4:
Examples / 14.5:
Differential Games / 15:
Two-Person Deterministic Continuous Differential Games / 15.1:
Two-Person Zero-Sum Differential Games / 15.2:
Pursuit Games / 15.3:
Coordination Differential Games / 15.4:
Noncooperative Differential Games / 15.5:
APPLICATIONS OF DYNAMIC OPTIMIZATION / Part 5:
Optimal Economic Growth / 16:
The Neoclassical Growth Model / 16.1:
Neoclassical Optimal Economic Growth / 16.2:
The Two Sector Growth Model / 16.3:
Heterogeneous Capital Goods / 16.4:
Appendices
Analysis / Appendix A:
Sets / A.1:
Relations and Functions / A.2:
Metric Spaces / A.3:
Vector Spaces / A.4:
Convex Sets and Functions / A.5:
Differential Calculus / A.6:
Differential Equations / A.7:
Matrices / Appendix B:
Basic Definitions and Examples / B.1:
Some Special Matrices / B.2:
Matrix Relations and Operations / B.3:
Scalar Valued Functions Defined on Matrices / B.4:
Inverse Matrix / B.5:
Linear Equations and Linear Inequalities / B.6:
Linear Transformations; Characteristic Roots and Vectors / B.7:
Quadratic Forms / B.8:
Matrix Derivatives / B.9:
Index
Preface to the Classics Edition
Preface
Introduction / Part 1:
3.

図書

図書
Martin Grötschel, Sven O. Krumke, Jörg Rambau, editors
出版情報: Berlin : Springer-Verlag, c2001  xii, 801 p. ; 25 cm
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4.

図書

図書
edited by Xiaoqi Yang and Kok Lay Teo and Lou Caccetta
出版情報: Dordrecht : Kluwer Academic Publishers, c2001  xxxvii, 412 p. ; 25 cm
シリーズ名: Applied optimization ; vol. 52
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5.

図書

図書
Thomas F. Edgar, David M. Himmelblau, Leon S. Lasdon
出版情報: New York : McGraw-Hill, 2001  xv, 651 p. ; 24 cm
シリーズ名: McGraw-Hill chemical engineering series
McGraw-Hill higher education
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6.

図書

図書
edited by Panos M. Pardalos and Mauricio G.C. Resende
出版情報: New York ; Tokyo : Oxford University Press, 2002  xviii, 1095 p. ; 26 cm
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7.

図書

図書
Andrzej Ruszczyński
出版情報: Princeton, N.J. : Princeton University Press, c2006  xii, 448 p. ; 24 cm
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8.

図書

図書
Yann Collette, Patrick Siarry
出版情報: Berlin ; New York : Springer, c2003  ix, 293 p. ; 24 cm
シリーズ名: Decision engineering
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Introduction: Multiobjective Optimization and Domination
Scalar Methods
Interactive Methods
Fuzzy Methods
Methods which use a Metaheuristic
Decision Aid Methods
Performances Measurement
Test Functions of Multiobjective Optimization Methods
Attempt to Classify Multiobjective Optimization Methods
Qualification of Scientific Software / Case Study No.1:
Study of the Extension of a Telecommunication Network / Case Study No.2:
Multicriteria Decision Tools to Deal with Bids / Case Study No.3:
Conclusion
References
Index
Introduction: Multiobjective Optimization and Domination
Scalar Methods
Interactive Methods
9.

図書

図書
Kenneth Lange
出版情報: New York ; Tokyo : Springer, c2004  xiii, 252 p. ; 25 cm
シリーズ名: Springer texts in statistics
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10.

図書

図書
Kevin M. Passino
出版情報: London : Springer, c2005  xxxi, 926 p. ; 24 cm
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