Functional Analysis, Calculus of Variations and Optimal Control

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ISBN: 978-1-4471-4819-7 (Print) 978-1-4471-4820-3 (Online)

Table of contents (26 chapters)

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  1. Front Matter

    Pages I-XIV

  2. Functional Analysis

    1. Front Matter

      Pages 1-1

    2. No Access

      Book Chapter

      Pages 3-25

      Normed Spaces

    3. No Access

      Book Chapter

      Pages 27-46

      Convex sets and functions

    4. No Access

      Book Chapter

      Pages 47-58

      Weak topologies

    5. No Access

      Book Chapter

      Pages 59-74

      Convex analysis

    6. No Access

      Book Chapter

      Pages 75-103

      Banach spaces

    7. No Access

      Book Chapter

      Pages 105-131

      Lebesgue spaces

    8. No Access

      Book Chapter

      Pages 133-155

      Hilbert spaces

    9. No Access

      Book Chapter

      Pages 157-169

      Additional exercises for Part I

  3. Optimization and Nonsmooth Analysis

    1. Front Matter

      Pages 171-171

    2. No Access

      Book Chapter

      Pages 173-191

      Optimization and multipliers

    3. No Access

      Book Chapter

      Pages 193-225

      Generalized gradients

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      Book Chapter

      Pages 227-254

      Proximal analysis

    5. No Access

      Book Chapter

      Pages 255-272

      Invariance and monotonicity

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      Book Chapter

      Pages 273-283

      Additional exercises for Part II

  4. Calculus of Variations

    1. Front Matter

      Pages 285-285

    2. No Access

      Book Chapter

      Pages 287-305

      The classical theory

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      Book Chapter

      Pages 307-318

      Nonsmooth extremals

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      Book Chapter

      Pages 319-334

      Absolutely continuous solutions

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      Book Chapter

      Pages 335-346

      The multiplier rule

    6. No Access

      Book Chapter

      Pages 347-366

      Nonsmooth Lagrangians

    7. No Access

      Book Chapter

      Pages 367-390

      Hamilton-Jacobi methods

    8. No Access

      Book Chapter

      Pages 391-414

      Multiple integrals

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