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1.

図書
図書
1. Compact convex sets and boundary integrals (: gw ; : us ; : pbk)
[by] Erik M. Alfsen
出版情報: Berlin ; New York : Springer-Verlag, 1971  ix, 210 p. ; 24 cm
シリーズ名: Ergebnisse der Mathematik und ihrer Grenzgebiete ; Bd. 57
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2.

図書
図書
2. Etude géométrique des espaces vectoriels (1 : gw - 2 : us)
Jacques Bair, René Fourneau
出版情報: Berlin ; New York : Springer-Verlag, 1975-1980  2 v. ; 25 cm
シリーズ名: Lecture notes in mathematics ; 489, 802
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目次情報:
[1] Une introduction
2. Polyèdres et polytopes convexes
[1] Une introduction
2. Polyèdres et polytopes convexes
3.

図書
図書
3. Geometric aspects of convex sets with the Radon-Nikodým property (: Berlin ; : New York)
Richard D. Bourgin
出版情報: Berlin ; New York : Springer-Verlag, 1983  xii, 474 p. ; 24 cm
シリーズ名: Lecture notes in mathematics ; 993
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4.

図書
図書
4. Convex analysis : an introductory text (pbk.)
Jan van Tiel
出版情報: Chichester [West Sussex] ; New York : Wiley, c1984  viii, 125 p. ; 24 cm
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5.

図書
図書
5. Convexity theory and its applications in functional analysis
L. Asimow, A.J. Ellis
出版情報: London ; New York : Academic Press, 1980  x, 266 p. ; 24 cm
シリーズ名: L.M.S. monographs ; no. 16
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6.

図書
図書
6. Convex sets and their applications
Steven R. Lay
出版情報: New York : Wiley, c1982  xvi, 244 p. ; 25 cm
シリーズ名: Pure and applied mathematics : a Wiley-Interscience series of texts, monographs, and tracts
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目次情報: 続きを見る
Fundamentals / 1：
Linear Algebra and Topology
Convex Sets / 2：
Hyperplanes
Hyperplanes and Linear Functionals / 3：
Separating Hyperplanes / 4：
Supporting Hyperplanes / 5：
Helly-Type Theorems
Helly's Theorem / 6：
Kirchberger's Theorem / 7：
Kirchberger-type Theorems
Separation by a Spherical Surface / 8：
Separation by a Cylinder / 9：
Separation by a Parallelotope / 10：
Special Topics in E[superscript 2]
Sets of Constant Width / 11：
Universal Covers / 12：
The Isoperimetric Problem / 13：
Families of Convex Sets
Parallel Bodies / 14：
The Blaschke Selection Theorem / 15：
The Existence of Extremal Sets / 16：
Characterizations of Convex Sets
Local Convexity / 17：
Local Support Properties / 18：
Nearest-Point Properties / 19：
Polytopes
The Faces of a Polytope / 20：
Special Types of Polytopes and Euler's Formula / 21：
Approximation by Polytopes / 22：
Duality
Polarity and Polytopes / 23：
Dual Cones / 24：
Optimization
Finite Matrix Games / 25：
Linear Programming / 26：
The Simplex Method / 27：
Convex Functions
Basic Properties / 28：
Support and Distance Functions / 29：
Continuity and Differentiability / 30：
Solutions, Hints, and References for Exercises
Bibliography
Index
Fundamentals / 1：
Linear Algebra and Topology
Convex Sets / 2：
7.

図書
図書
7. Convex analysis and global optimization
by Hoang Tuy
出版情報: Dordrecht : Kluwer Academic Publishers, c1998  xi, 339 p. ; 25 cm
シリーズ名: Nonconvex optimization and its applications ; v. 22
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8.

図書
図書
8. Abstract convex analysis
Ivan Singer
出版情報: New York : John Wiley & Sons, c1997  xix, 491 p. ; 25 cm
シリーズ名: Canadian Mathematical Society series of monographs and advanced texts
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目次情報: 続きを見る
Abstract Convexity of Elements of a Complete Lattice
Abstract Convexity of Subsets of a Set
Abstract Convexity of Functions on a Set
Abstract Quasi-Convexity of Functions on a Set
Dualities Between Complete Lattices
Dualities Between Families of Subsets
Dualities Between Sets of Functions
Conjugations. (-Dualities and <$$$>-Dualities
Abstract Subdifferentials
Notes and Remarks
References
Indexes
Abstract Convexity of Elements of a Complete Lattice
Abstract Convexity of Subsets of a Set
Abstract Convexity of Functions on a Set
9.

図書
図書
9. Foundations of mathematical optimization : convex analysis without linearity
by Diethard Pallaschke and Stefan Rolewicz
出版情報: Dordrecht ; Boston : Kluwer Academic, c1997  xii, 582 p. ; 25 cm
シリーズ名: Mathematics and its applications ; v. 388
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10.

図書
図書
10. Geometric applications of Fourier series and spherical harmonics
H. Groemer
出版情報: Cambridge ; New York : Cambridge University Press, 1996  xi, 329 p. ; 24 cm
シリーズ名: Encyclopedia of mathematics and its applications / edited by G.-C. Rota ; v. 61
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11.

図書
図書
11. Konvexe Analysis
Jürg T. Marti
出版情報: Basel ; Stuttgart : Birkhäuser, 1977  xi, 273 p. ; 25 cm
シリーズ名: Lehrbücher und Monographien aus dem Gebiete der exakten Wissenschaften ; . Mathematische Reihe
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12.

図書
図書
12. Convex sets
[by] Frederick A. Valentine
出版情報: New York : McGraw-Hill, [1964]  ix, 238 p. ; 24 cm
シリーズ名: McGraw-Hill series in higher mathematics
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13.

図書
図書
13. Convexity and its applications
edited by Peter M. Gruber, Jörg M. Wills
出版情報: Basel [Switzerland] ; Boston : Birkhäuser, 1983  421 p. ; 25 cm
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14.

図書
図書
14. Geometric functional analysis and its applications (us ; gw)
Richard B. Holmes
出版情報: New York : Springer-Verlag, [1975]  x, 246 p. ; 25 cm
シリーズ名: Graduate texts in mathematics ; 24
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15.

図書
図書
15. Polyèdres et polytopes convexes
Bair, Jacques ; Fourneau, René
出版情報: Berlin ; New York : Springer-Verlag, 1980  vi, 282 p.
シリーズ名: Lecture notes in mathematics ; 802 . Etude géometrique des espaces vectoriels / Jacques Bair, René Fourneau ; 2
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16.

図書
図書
16. Convex analysis and nonlinear geometric elliptic equations (: Berlin ; : New York)
Ilya J. Bakelman
出版情報: Berlin ; New York : Springer-Verlag, c1994  xxi, 510 p. ; 25 cm
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17.

図書
図書
17. Convexity
Roger Webster
出版情報: Oxford ; Tokyo : Oxford University Press, 1994  xvii, 444 p. ; 24 cm
シリーズ名: Oxford science publications
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18.

図書
図書
18. Fundamentals of convex analysis : duality, separation, representation, and resolution
by Michael J. Panik
出版情報: Dordrecht ; Boston : Kluwer Academic Publishers, c1993  xxii, 294 p. ; 25 cm
シリーズ名: Theory and decision library ; series B . Mathematical and statistical methods ; v. 24
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19.

図書
図書
19. Selecta
Heinz Bauer ; edited by Herbert Heyer, Niels Jacob, Ivan Netuka
出版情報: Berlin : Walter de Gruyter, 2003  xiv, 597 p. ; 25 cm
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20.

図書
図書
20. Fourier analysis in convex geometry
Alexander Koldobsky
出版情報: Providence, R.I. : American Mathematical Society, c2005  vi, 170 p. ; 26 cm
シリーズ名: Mathematical surveys and monographs ; v. 116
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21.

図書
図書
21. Fundamentals of convex analysis
Jean-Baptiste Hiriart-Urruty, Claude Lemaréchal
出版情報: Berlin : Springer, c2001  x, 259 p. ; 24 cm
シリーズ名: Grundlehren text editions / editors, A. Chenciner ... [et al.] ; managing editors, M. Berger, J. Coates, S.R.S. Varadhan
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目次情報: 続きを見る
Preface
Introduction: Notation, Elementary Results / 0：
Some Facts About Lower and Upper Bounds / 1：
The Set of ExtendedReal Numbers / 2：
Linear and Bilinear Algebra / 3：
Differentiationin a Euclidean Space / 4：
Set-Valued Analysis / 5：
Recalls on Convex Functions of the Real Variable / 6：
Exercises
Convex Sets / A：
Generalities
Definition and First Examples / 1.1：
Convexity-PreservingOperationsonSets / 1.2：
ConvexCombinationsandConvexHulls / 1.3：
ClosedConvexSetsandHulls / 1.4：
ConvexSetsAttachedtoaConvexSet
TheRelativeInterior / 2.1：
TheAsymptoticCone / 2.2：
ExtremePoints / 2.3：
Exposed Faces / 2.4：
ProjectionontoClosedConvexSets
TheProjectionOperator / 3.1：
ProjectionontoaClosedConvexCone / 3.2：
Separation and Applications
SeparationBetweenConvexSets / 4.1：
First Consequences of the Separation Properties / 4.2：
Existence of Supporting Hyperplanes
Outer Description of Closed ConvexSets
Proof of Minkowski's Theorem
Bipolar of a ConvexCone
The Lemma of Minkowski-Farkas / 4.3：
ConicalApproximationsofConvexSets
ConvenientDefinitions of Tangent Cones / 5.1：
TheTangentandNormalConestoaConvexSet / 5.2：
SomePropertiesofTangentandNormalCones / 5.3：
Convex Functions / B：
Basic Definitions and Examples
The Definitions of a ConvexFunction
Special Convex Functions: Affinity and Closedness
Linear and Affine Functions
ClosedConvexFunctions
OuterConstructionofClosedConvexFunctions
FirstExamples
FunctionalOperationsPreservingConvexity
OperationsPreservingClosedness
Dilations and Perspectives of a Function
Infimal Convolution
Image of a Function Under a Linear Mapping
Convex Hull and Closed Convex Hull of a Function / 2.5：
Local and Global Behaviour of a Convex Function
Continuity Properties
Behaviour at Infinity
First- and Second-Order Differentiation
Differentiable ConvexFunctions
Nondifferentiable Convex Functions
Second-Order Differentiation
Sublinearity and Support Functions / C：
SublinearFunctions
Definitions and First Propertie
SomeExamples
TheConvexConeofAllClosedSublinearFunctions
The Support Function of a Nonempty Set
Definitions, Interpretations
BasicProperties
Examples
Correspondence Between Convex Sets and Sublinear Functions
The Fundamental Correspondence
Example: Norms and Their Duals, Polarity
Calculus with Support Functions / 3.3：
Example: Support Functions of Closed Convex Polyhedra / 3.4：
Subdifferentials of Finite Convex Functions / D：
The Subdifferential: Definitions and Interpretations
First Definition: Directional Derivatives
Second Definition: Minorizationby Affine Functions
GeometricConstructionsandInterpretations
Local Properties of the Subdifferential
First-OrderDevelopments
Minimality Conditions
Mean-ValueTheorems
Calculus Rules with Subdifferentials
Positive Combinations of Functions
Pre-Composition with an Affine Mapping
Post-Composition with an Increasing Convex Function of Several Variables
Supremum of Convex Functions / 4.4：
FurtherExamples / 4.5：
Largest Eigenvalue of a Symmetric Matrix
NestedOptimization
Best Approximation of a Continuous Function on a Compact Interval
The Subdifferential as a Multifunction
Monotonicity Properties of the Subdifferential / 6.1：
Continuity Properties of the Subdifferential / 6.2：
Subdifferentials and Limits of Subgradients / 6.3：
Conjugacy in Convex Analysis / E：
The Convex Conjugate of a Function
Interpretations
FirstProperties
-Elementary Calculus Rules
-The Biconjugate of a Function
-ConjugacyandCoercivity
Subdifferentials of Extended-Valued Functions
Calculus Rules on the Conjugacy Operation
Sum of Two Functions
Infima and Suprema
Post-Composition with an Increasing Convex Function
Various Examples
The Cramer Transformation
The Conjugate of Convex Partially Quadratic Functions
PolyhedralFunctions
Differentiability of a Conjugate Function
First-Order Differentiability
Lipschitz Continuity of the Gradient Mapping
Bibliographical Comments
The Founding Fathers of the Discipline
References
Index
Preface
Introduction: Notation, Elementary Results / 0：
Some Facts About Lower and Upper Bounds / 1：
22.

図書
図書
22. Convex analysis and minimization algorithms (1 : gw - 2 : us)
Jean-Baptiste Hiriart-Urruty, Claude Lemaréchal
出版情報: Berlin ; New York ; Tokyo : Springer-Verlag, c1993  2 v. ; 25 cm
シリーズ名: Die Grundlehren der mathematischen Wissenschaften ; 305, 306
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23.

電子ブック
ＥＢ
23. Large-scale convex optimization : : algorithms & analyses via monotone operators ((ebook))
Ernest K. Ryu, Wotao Yin
出版情報:   1 online resource (xiv, 303 pages)
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