Convex Analysis and Minimization Algorithms I

1. Front Matter

   Pages I-XVII

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2. Convex Functions of One Real Variable

   • Jean-Baptiste Hiriart-Urruty, Claude Lemaréchal

   Pages 1-46

3. Introduction to Optimization Algorithms

   • Jean-Baptiste Hiriart-Urruty, Claude Lemaréchal

   Pages 47-86

4. Convex Sets

   • Jean-Baptiste Hiriart-Urruty, Claude Lemaréchal

   Pages 87-141

5. Convex Functions of Several Variables

   • Jean-Baptiste Hiriart-Urruty, Claude Lemaréchal

   Pages 143-193

6. Sublinearity and Support Functions

   • Jean-Baptiste Hiriart-Urruty, Claude Lemaréchal

   Pages 195-236

7. Subdifferentials of Finite Convex Functions

   • Jean-Baptiste Hiriart-Urruty, Claude Lemaréchal

   Pages 237-289

8. Constrained Convex Minimization Problems: Minimality Conditions, Elements of Duality Theory

   • Jean-Baptiste Hiriart-Urruty, Claude Lemaréchal

   Pages 291-341

9. Descent Theory for Convex Minimization: The Case of Complete Information

   • Jean-Baptiste Hiriart-Urruty, Claude Lemaréchal

   Pages 343-384

10. Back Matter

    Pages 385-420

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Convex Analysis may be considered as a refinement of standard calculus, with equalities and approximations replaced by inequalities. As such, it can easily be integrated into a graduate study curriculum. Minimization algorithms, more specifically those adapted to non-differentiable functions, provide an immediate application of convex analysis to various fields related to optimization and operations research. These two topics making up the title of the book, reflect the two origins of the authors, who belong respectively to the academic world and to that of applications. Part I can be used as an introductory textbook (as a basis for courses, or for self-study); Part II continues this at a higher technical level and is addressed more to specialists, collecting results that so far have not appeared in books.

• Convex Analysis
• Mathematical Programming
• Nonsmooth Optimization
• Numerical Algorithms
• algorithms
• operations research
• optimization

From the reviews: "... The book is very well written, nicely illustrated, and clearly understandable even for senior undergraduate students of mathematics... Throughout the book, the authors carefully follow the recommendation by A. Einstein: 'Everything should be made as simple as possible, but not simpler.'"

• Département de Mathématiques, Université Paul Sabatier, Toulouse, France

  Jean-Baptiste Hiriart-Urruty

• Rocquencourt, Domaine de Voluceau, INRIA, Le Chesnay, France

  Claude Lemaréchal

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