| Description |
1 online resource |
| Contents |
Ch. 1. Preliminary results on functional analysis. 1.1. Preliminary notions and results. 1.2. Closedness and interiority notions. 1.3. Open mapping theorems. 1.4. Variational principles. 1.5. Exercises. 1.6. Bibliographical notes -- ch. 2. Convex analysis in locally convex spaces. 2.1. Convex functions. 2.2. Semi-continuity of convex functions. 2.3. Conjugate functions. 2.4. The subdifferential of a convex function. 2.5. The general problem of convex programming. 2.6. Perturbed problems. 2.7. The fundamental duality formula. 2.8. Formulas for conjugates and e-subdifferentials, duality relations and optimality conditions. 2.9. Convex optimization with constraints. 2.10. A minimax theorem. 2.11. Exercises. 2.12. Bibliographical notes -- ch. 3. Some results and applications of convex analysis in normed spaces. 3.1. Further fundamental results in convex analysis. 3.2. Convexity and monotonicity of subdifferentials. 3.3. Some classes of functions of a real variable and differentiability of convex functions. 3.4. Well conditioned functions. 3.5. Uniformly convex and uniformly smooth convex functions. 3.6. Uniformly convex and uniformly smooth convex functions on bounded sets. 3.7. Applications to the geometry of normed spaces. 3.8. Applications to the best approximation problem. 3.9. Characterizations of convexity in terms of smoothness. 3.10. Weak sharp minima, well-behaved functions and global error bounds for convex inequalities. 3.11. Monotone multifunctions. 3.12. Exercises. 3.13. Bibliographical notes |
| Summary |
The primary aim of this book is to present the conjugate and subdifferential calculus using the method of perturbation functions in order to obtain the most general results in this field. The secondary aim is to provide important applications of this calculus and of the properties of convex functions. Such applications are: the study of well-conditioned convex functions, uniformly convex and uniformly smooth convex functions, best approximation problems, characterizations of convexity, the study of the sets of weak sharp minima, well-behaved functions and the existence of global error bounds f |
| Notes |
Print version record |
| Subject |
Convex functions.
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Convex sets.
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Functional analysis.
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Vector spaces.
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Convex functions
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Convex sets
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Functional analysis
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Vector spaces
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| Form |
Electronic book
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| ISBN |
1299604455 |
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9781299604452 |
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9789812777096 |
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9812777091 |
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