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1.

図書
図書
1. Introduction to optimization techniques : fundamentals and applications of nonlinear programming
Masanao Aoki
出版情報: New York : Macmillan, c1971  xvi, 335 p. ; 24 cm
シリーズ名: Macmillan series in applied computer sciences
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2.

図書
図書
2. Nonlinear programming : analysis and methods
Mordecai Avriel
出版情報: Englewood Cliffs, N.J. : Prentice-Hall, c1976  xv, 512 p. ; 24 cm
シリーズ名: Prentice-Hall series in automatic computation
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3.

図書
図書
3. Nonlinear programming : theory and algorithms
Mokhtar S. Bazaraa, C.M. Shetty
出版情報: New York : Wiley, c1979  xiv, 560 p. ; 24 cm
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目次情報: 続きを見る
Introduction. / Chapter 1：
Problem Statement and Basic Definitions / 1.1：
Illustrative Examples / 1.2：
Guidelines for Model Construction / 1.3：
Exercises
Notes and References
Convex Analysis. / Part 1：
Convex Sets. / Chapter 2：
Convex Hulls / 2.1：
Closure and Interior of a Set / 2.2：
Weierstrass's Theorem / 2.3：
Separation and Support of Sets / 2.4：
Convex Cones and Polarity / 2.5：
Polyhedral Sets, Extreme Points, and Extreme Directions / 2.6：
Linear Programming and the Simplex Method / 2.7：
Convex Functions and Generalizations. / Chapter 3：
Definitions and Basic Properties / 3.1：
Subgradients of Convex Functions / 3.2：
Differentiable Convex Functions / 3.3：
Minima and Maxima of Convex Functions / 3.4：
Generalizations of Convex Functions / 3.5：
Optimality Conditions and Duality. / Part 2：
The Fritz John and Karush-Kuhn-Tucker Optimality Conditions. / Chapter 4：
Unconstrained Problems / 4.1：
Problems Having Inequality Constraints / 4.2：
Problems Having Inequality and Equality Constraints / 4.3：
Second-Order Necessary and Sufficient Optimality Conditions for Constrained Problems / 4.4：
Constraint Qualifications. / Chapter 5：
Cone of Tangents / 5.1：
Other Constraint Qualifications / 5.2：
Lagrangian Duality and Saddle Point Optimality Conditions. / 5.3：
Lagrangian Dual Problem / 6.1：
Duality Theorems and Saddle Point Optimality Conditions / 6.2：
Properties of the Dual Function / 6.3：
Formulating and Solving the Dual Problem / 6.4：
Getting the Primal Solution / 6.5：
Linear and Quadratic Programs / 6.6：
Algorithms and Their Convergence / Part 3：
The Concept of an Algorithm. / Chapter 7：
Algorithms and Algorithmic Maps / 7.1：
Closed Maps and Convergence / 7.2：
Composition of Mappings / 7.3：
Comparison Among Algorithms / 7.4：
Unconstrained Optimization. / Chapter 8：
Line Search Without Using Derivatives / 8.1：
Line Search Using Derivatives / 8.2：
Some Practical Line Search Methods / 8.3：
Closedness of the Line Search Algorithmic Map / 8.4：
Multidimensional Search Without Using Derivatives / 8.5：
Multidimensional Search Using Derivatives / 8.6：
Modification of Newton's Method: Levenberg-Marquardt and Trust Region Methods / 8.7：
Methods Using Conjugate Directions: Quasi-Newton and Conjugate Gradient Methods / 8.8：
Subgradient Optimization Methods / 8.9：
Penalty and Barrier Functions. / Chapter 9：
Concept of Penalty Functions / 9.1：
Exterior Penalty Function Methods / 9.2：
Exact Absolute Value and Augmented Lagrangian Penalty Methods / 9.3：
Barrier Function Methods / 9.4：
Polynomial-Time Interior Point Algorithms for Linear Programming Based on a Barrier Function / 9.5：
Methods of Feasible Directions. / Chapter 10：
Method of Zoutendijk / 10.1：
Convergence Analysis of the Method of Zoutendijk / 10.2：
Successive Linear Programming Approach / 10.3：
Successive Quadratic Programming or Projected Lagrangian Approach / 10.4：
Gradient Projection Method of Rosen / 10.5：
Reduced Gradient Method of Wolfe and Generalized Reduced Gradient Method / 10.6：
Convex-Simplex Method of Zangwill / 10.7：
Effective First- and Second-Order Variants of the Reduced Gradient Method / 10.8：
Linear Complementary Problem, and Quadratic, Separable, Fractional, and Geometric Programming. / Chapter 11：
Linear Complementary Problem / 11.1：
Convex and Nonconvex Quadratic Programming: Global Optimization Approaches / 11.2：
Separable Programming / 11.3：
Linear Fractional Programming / 11.4：
Geometric Programming / 11.5：
Mathematical Review. / Appendix A：
Summary of Convexity, Optimality Conditions, and Duality. / Appendix B：
Bibliography.
Index
Introduction. / Chapter 1：
Problem Statement and Basic Definitions / 1.1：
Illustrative Examples / 1.2：
4.

図書
図書
4. An algorithmic approach to nonlinear analysis and optimization
[by] Edward J. Beltrami
出版情報: New York : Academic Press, 1970  xiv, 235 p. ; 24 cm
シリーズ名: Mathematics in science and engineering : a series of monographs and textbooks ; v. 63
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5.

図書
図書
5. The mathematics of nonlinear programming (: us ; : gw)
Anthony L. Peressini, Francis E. Sullivan, J. Jerry Uhl, Jr.
出版情報: New York ; Tokyo : Springer-Verlag, c1988  x, 273 p. ; 25 cm
シリーズ名: Undergraduate texts in mathematics
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目次情報: 続きを見る
Preface
Unconstrained Optimization via Calculus / 1：
Convex and Convex Functions / 2：
Iterative Methods for Unconstrained Optimization / 3：
Least Squares Optimization / 4：
Convex Programming and the Karush-Kuhn-Tucker Conditions / 5：
Penalty Methods / 6：
Optimization with Equality Constraints / 7：
Index
Preface
Unconstrained Optimization via Calculus / 1：
Convex and Convex Functions / 2：
6.

図書
図書
6. Studies in linear and non-linear programming (: hard ; : pbk)
by Kenneth J. Arrow, Leonid Hurwicz, Hirofumi Uzawa ; with contributions by Hollis B. Chenery ... [et al.]
出版情報: Stanford, Calif. : Stanford University Press, 1958  229 p. ; 26 cm
シリーズ名: Stanford mathematical studies in the social sciences ; 2
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7.

図書
図書
7. Nonlinear programming
editor, J. Abadie ; contributors, S. Vajda ... [et al.]
出版情報: Amsterdam : North-Holland, 1967  xxii, 316 p. ; 23 cm
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8.

図書
図書
8. Nonlinear programming : sequential unconstrained minimization techniques
[by] Anthony V. Fiacco [and] Garth P. McCormick
出版情報: New York : Wiley, c1968  xiv, 210 p. ; 23 cm
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9.

図書
図書
9. Constrained global optimization : algorithms and applications (: gw ; : us)
P.M. Pardalos, J.B. Rosen
出版情報: Berlin ; Tokyo : Springer-Verlag, c1987  vii, 143 p. ; 25 cm
シリーズ名: Lecture notes in computer science ; 268
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10.

図書
図書
10. Nondifferentiable optimization and polynomial problems
Naum Z. Shor
出版情報: Boston : Kluwer, 1998  xvii, 394p ; 25cm
シリーズ名: Nonconvex optimization and its applications ; v. 24
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