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1.

図書
図書
1. 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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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.：
2.

図書
図書
2. 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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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：
3.

図書
図書
3. 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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4.

図書
図書
4. Convex optimization
Stephen Boyd, Lieven Vandenberghe
出版情報: Cambridge : Cambridge University Press, 2004  xiii, 716 p. ; 26 cm
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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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