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1.

図書
図書
1. 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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2.

図書
図書
2. Convex analysis and variational problems (: us ; : ne)
Ivar Ekeland, Roger Temam
出版情報: Amsterdam : North-Holland Pub. Co. , New York : distributors for the U.S.A., American Elsevier Pub. Co., 1976  ix, 402 p. ; 23 cm
シリーズ名: Studies in mathematics and its applications ; v. 1
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3.

図書
図書
3. Convex analysis and optimization
ed. by J.P. Aubin & R.B. Vinter
出版情報: Boston : Pitman Advanced Pub. Program, c1982  210 p. ; 25 cm
シリーズ名: Research notes in mathematics ; 57
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目次情報: 続きを見る
Ioffe's fans and generalized derivatives of vector-valued maps / J.-P. Aubin
A review of continuity and differentiability properties of quasiconvex functions on (Rn) / J.-P. Crouzeix
Ioffe's mean value theorem / I. Ekeland
(E-) subdifferential calculus / J.-B. Hiriart-Urruty
Non-smooth analysis and the theory of fans / A.D. Ioffe
The invariance of the absolute Borel classes / J.E. Jayne and C.A. Rogers
Convex functions arising in optimal control, and Ioffe's global optimally conditions / R.B. Vinter
New applications of generalized curves, particularly in physics/ L.C. Young
Ioffe's fans and generalized derivatives of vector-valued maps / J.-P. Aubin
A review of continuity and differentiability properties of quasiconvex functions on (Rn) / J.-P. Crouzeix
Ioffe's mean value theorem / I. Ekeland
4.

図書
図書
4. Holomorphy and convexity in Lie theory
by Karl-Hermann Neeb
出版情報: Berlin : Walter de Gruyter, 2000, c1999  xxi, 778 p. ; 25 cm
シリーズ名: De Gruyter expositions in mathematics ; v. 28
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目次情報: 続きを見る
Preface
Introduction
Abstract Representation Theory / A.：
Reproducing Kernel Spaces / Chapter I.：
Operator-Valued Positive Definite Kernels / I.1.：
The Cone of Positive Definite Kernels / I.2.：
Representations of Involutive Semigroups / Chapter II.：
Involutive Semigroups / II.1.：
Bounded Representations / II.2.：
Hermitian Representations / II.3.：
Representations on Reproducing Kernel Spaces / II.4.：
Positive Definite Functions on Involutive Semigroups / Chapter III.：
Positive Definite Functions--the Discrete Case / III.1.：
Enveloping C*-algebras / III.2.：
Multiplicity Free Representations / III.3.：
Continuous and Holomorphic Representations / Chapter IV.：
Continuous Representations and Positive Definite Functions / IV.1.：
Holomorphic Representations of Involutive Semigroups / IV.2.：
Convex Geometry and Representations of Vector Spaces / B.：
Convex Sets and Convex Functions / Chapter V.：
Convex Sets and Cones / V.1.：
Finite Reflection Groups and Convex Sets / V.2.：
Convex Functions and Fenchel Duality / V.3.：
Laplace Transforms / V.4.：
The Characteristic Function of a Convex Set / V.5.：
Representations of Cones and Tubes / Chapter VI.：
Commutative Representation Theory / VI.1.：
Representations of Cones / VI.2.：
Holomorphic Representations of Tubes / VI.3.：
Realization of Cyclic Representations by Holomorphic Functions / VI.4.：
Holomorphic Extensions of Unitary Representations / VI.5.：
Convex Geometry of Lie Algebras / C.：
Convexity in Lie Algebras / Chapter VII.：
Compactly Embedded Cartan Subalgebras / VII.1.：
Root Decompositions / VII.2.：
Lie Algebras With Many Invariant Convex Sets / VII.3.：
Convexity Theorems and Their Applications / Chapter VIII.：
Admissible Coadjoint Orbits and Convexity Theorems / VIII.1.：
The Structure of Admissible Lie Algebras / VIII.2.：
Invariant Elliptic Cones in Lie Algebras / VIII.3.：
Highest Weight Representations of Lie Algebras, Lie Groups, and Semigroups / D.：
Unitary Highest Weight Representations: Algebraic Theory / Chapter IX.：
Generalized Highest Weight Representations / IX.1.：
Positive Complex Polarizations / IX.2.：
Highest Weight Modules of Finite-Dimensional Lie Algebras / IX.3.：
The Metaplectic Factorization / IX.4.：
Unitary Highest Weight Representations of Hermitian Lie Algebras / IX.5.：
Unitary Highest Weight Representations: Analytic Theory / Chapter X.：
The Convex Moment Set of a Unitary Representation / X.1.：
Irreducible Unitary Representations / X.2.：
The Metaplectic Representation and Its Applications / X.3.：
Special Properties of Unitary Highest Weight Representations / X.4.：
Moment Sets for C*-algebras / X.5.：
Moment Sets for Group Representations / X.6.：
Complex Ol'shanskii Semigroups and Their Representations / Chapter XI.：
Lawson's Theorem on Ol'shanskii Semigroups / XI.1.：
Holomorphic Extension of Unitary Representations / XI.2.：
Holomorphic Representations of Ol'shanskii Semigroups / XI.3.：
Irreducible Holomorphic Representations / XI.4.：
Gelfand-Raikov Theorems for Ol'shanskii Semigroups / XI.5.：
Decomposition and Characters of Holomorphic Representations / XI.6.：
Realization of Highest Weight Representations on Complex Domains / Chapter XII.：
The Structure of Groups of Harish-Chandra Type / XII.1.：
Representations of Groups of Harish-Chandra Type / XII.2.：
The Compression Semigroup and Its Representations / XII.3.：
Examples / XII.4.：
Hilbert Spaces of Square Integrable Holomorphic Functions / XII.5.：
Complex Geometry and Representation Theory / E.：
Complex and Convex Geometry of Complex Semigroups / Chapter XIII.：
Locally Convex Functions and Local Recession Cones / XIII.1.：
Invariant Convex Sets and Functions in Lie Algebras / XIII.2.：
Calculations in Low-Dimensional Cases / XIII.3.：
Biinvariant Plurisubharmonic Functions / XIII.4.：
Complex Semigroups and Stein Manifolds / XIII.5.：
Biinvariant Domains of Holomorphy / XIII.6.：
Biinvariant Hilbert Spaces and Hardy Spaces on Complex Semigroups / Chapter XIV.：
Biinvariant Hilbert Spaces / XIV.1.：
Hardy Spaces Defined by Sup-Norms / XIV.2.：
Hardy Spaces Defined by Square Integrability / XIV.3.：
The Fine Structure of Hardy Spaces / XIV.4.：
Coherent State Representations / Chapter XV.：
Complex Structures on Homogeneous Spaces / XV.1.：
Heisenberg's Uncertainty Principle and Coherent States / XV.2.：
Appendices
Bounded Operators on Hilbert Spaces / Appendix I.：
Spectral Measures and Unbounded Operators / Appendix II.：
Holomorphic Functions on Infinite-Dimensional Spaces / Appendix III.：
Symplectic Geometry / Appendix IV.：
Simple Modules of p-Length 2 / Appendix V.：
Symplectic Modules of Convex Type / Appendix VI.：
Square Integrable Representations of Locally Compact Groups / Appendix VII.：
The Stone-von Neumann-Mackey Theorem / Appendix VIII.：
Bibliography
List of Symbols
Index
Preface
Introduction
Abstract Representation Theory / A.：
5.

図書
図書
5. 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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6.

図書
図書
6. 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
7.

図書
図書
7. Convex functions
A. Wayne Roberts, Dale E. Varberg
出版情報: New York : Academic Press, 1973  xx, 300 p. ; 23 cm
シリーズ名: Pure and applied mathematics ; 57
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8.

図書
図書
8. Gâteaux differentiability of convex functions and topology : weak asplund spaces
Marián J. Fabian
出版情報: New York : Wiley, c1997  xi, 180 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
Canonical Examples of Weak Asplund Spaces
Properties of Gateaux Differentiability Spaces and Weak Asplund Spaces
Stegall's Classes
Two More Concrete Classes of Banach Spaces that Lie in S
Fragmentability
"Long Sequences" of Linear Projections
Vasak Spaces and Gul'ko Compacta
A Characterization of WCG Spaces and of Eberlein Compacta
Main Open Questions and Problems
References
Index
Canonical Examples of Weak Asplund Spaces
Properties of Gateaux Differentiability Spaces and Weak Asplund Spaces
Stegall's Classes
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. Subdifferentials : theory and applications
by A.G. Kusraev, S.S. Kutateladze
出版情報: Dordrecht ; Boston : Kluwer Academic Publishers, c1995  ix, 398 p. ; 25 cm
シリーズ名: Mathematics and its applications ; v. 323
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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. 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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13.

図書
図書
13. Convex analysis with application in the differentiation of convex functions (est.)
John R. Giles
出版情報: Boston : Pitman Pub., c1982  x, 278 p. ; 25 cm
シリーズ名: Research notes in mathematics ; 58
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14.

図書
図書
14. Convex functions, monotone operators and differentiability. 2nd ed (: us ; : gw)
Robert R. Phelps
出版情報: Berlin ; New York : Springer-Verlag, c1993  ix, 116 p. ; 24 cm
シリーズ名: Lecture notes in mathematics ; 1364
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15.

図書
図書
15. 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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16.

図書
図書
16. Convex functions and optimization methods on Riemannian manifolds
by Constantin Udrişte
出版情報: Dordrecht ; Boston : Kluwer Academic Publishers, c1994  xv, 348 p. ; 25 cm
シリーズ名: Mathematics and its applications ; v. 297
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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. Convex optimization in signal processing and communications
edited by Daniel P. Palomar and Yonina C. Eldar
出版情報: Cambridge ; Tokyo : Cambridge University Press, 2010  xiv, 498 p. ; 26 cm
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目次情報: 続きを見る
Automatic code generation for real-time convex optimization / J. Mattingley ; S. Boyd1：
Gradient-based algorithms with applications to signal recovery problems / A. Beck ; M. Teboulle2：
Graphical models of autoregressive processes / J. Songsiri ; J. Dahl ; L. Vandenberghe3：
SDP relaxation of homogeneous quadratic optimization / Z. Q. Luo ; T. H. Chang4：
Probabilistic analysis of SDR detectors for MIMO systems / A. Man-Cho So ; Y. Ye5：
Semidefinite programming, matrix decomposition, and radar code design / Y. Huang ; A. De Maio ; S. Zhang6：
Convex analysis for non-negative blind source separation with application in imaging / W. K. Ma ; T. H. Chan ; C. Y. Chi ; Y. Wang7：
Optimization techniques in modern sampling theory / T. Michaeli ; Y. C. Eldar8：
Robust broadband adaptive beamforming using convex optimization / M. RÃ1/4bsamen ; A. El-Keyi ; A. B. Gershman ; T. Kirubarajan9：
Cooperative distributed multi-agent optimization / A. NenadiÄç ; A. Ozdaglar10：
Competitive optimization of cognitive radio MIMO systems via game theory / G. Scutari ; D. P. Palomar ; S. Barbarossa11：
Nash equilibria: the variational approach / F. Facchinei ; J. S. Pang12：
Automatic code generation for real-time convex optimization / J. Mattingley ; S. Boyd1：
Gradient-based algorithms with applications to signal recovery problems / A. Beck ; M. Teboulle2：
Graphical models of autoregressive processes / J. Songsiri ; J. Dahl ; L. Vandenberghe3：
20.

図書
図書
20. 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：
21.

図書
図書
21. Convex functions and Orlicz spaces
M.A. Krasnoselʹskiĭ and Ya. B. Rutickiĭ ; translated from the first Russian edition by Leo F. Boron
出版情報: Groningen : P. Noordhoff, 1961  ix, 249 p. ; 23 cm
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22.

図書
図書
22. Introductory lectures on convex optimization : basic course
by Yurii Nesterov
出版情報: Boston : Kluwer Academic, c2004  xviii, 236 p. ; 24 cm
シリーズ名: Applied optimization ; v. 87
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23.

図書
図書
23. Convex functions and Orlicz spaces
[by] M.A. Krasnoselsky and Y.B. Rutitsky. Authorised translation from Russian
出版情報: Delhi : Hindustan Pub. Corpn, c1962  262 p ; 23 cm
シリーズ名: International monographs on advanced mathematics and physics
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24.

図書
図書
24. 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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25.

電子ブック
ＥＢ
25. 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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26.

図書
図書
26. Convex optimization
Stephen Boyd, Lieven Vandenberghe
出版情報: Cambridge : Cambridge University Press, 2004  xiii, 716 p. ; 26 cm
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目次情報: 続きを見る
Preface
Introduction / 1：
Theory / Part I：
Convex sets / 2：
Convex functions / 3：
Convex optimization problems / 4：
Duality / 5：
Applications / Part II：
Approximation and fitting / 6：
Statistical estimation / 7：
Geometrical problems / 8：
Algorithms / Part III：
Unconstrained minimization / 9：
Equality constrained minimization / 10：
Interior-point methods / 11：
Appendices
Preface
Introduction / 1：
Theory / Part I：
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