An Easy Path to Convex Analysis and Applications

1. Front Matter

   Pages i-xx

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2. Convex Sets and Functions

   • Boris Mordukhovich, Nguyen Mau Nam

   Pages 1-44

3. Convex Separation and Some Consequences

   • Boris Mordukhovich, Nguyen Mau Nam

   Pages 45-80

4. Convex Generalized Differentiation

   • Boris Mordukhovich, Nguyen Mau Nam

   Pages 81-119

5. Fenchel Conjugate and Further Topics in Subdifferentiation

   • Boris Mordukhovich, Nguyen Mau Nam

   Pages 121-150

6. Remarkable Consequences of Convexity

   • Boris Mordukhovich, Nguyen Mau Nam

   Pages 151-169

7. Minimal Time Functions and Related Issues

   • Boris Mordukhovich, Nguyen Mau Nam

   Pages 171-189

8. Applications to Problems of Optimization and Equilibrium

   • Boris Mordukhovich, Nguyen Mau Nam

   Pages 191-236

9. Applications to Location Problems

   • Boris Mordukhovich, Nguyen Mau Nam

   Pages 237-275

10. Back Matter

    Pages 277-300

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This book examines the most fundamental parts of convex analysis and its applications to optimization and location problems. Accessible techniques of variational analysis are employed to clarify and simplify some basic proofs in convex analysis and to build a theory of generalized differentiation for convex functions and sets in finite dimensions. The book serves as a bridge for the readers who have just started using convex analysis to reach deeper topics in the field. Detailed proofs are presented for most of the results in the book and also included are many figures and exercises for better understanding the material. Applications provided include both the classical topics of convex optimization and important problems of modern convex optimization, convex geometry, and facility location.

• Convex Set
• Convex Function
• Convex Analysis and Optimization
• Generalized Differentiation
• Fenchel Conjugate
• Facility Location

• Wayne State University, Detroit, USA

  Boris Mordukhovich

• Department of Mathematics and Sciences, Portland State University, Portland, USA

  Nguyen Mau Nam

Boris Mordukhovich, PhD, is Distinguished University Professor of Mathematics at Wayne State University. He has more than 500 publications including several monographs. Among his best known achievements are the introduction and development of powerful constructions of generalized differentiation and their applications to broad classes of problems in variational analysis, optimization, equilibrium, control, economics, engineering, and other fields. Dr. Mordukhovich is a SIAM Fellow, an AMS Fellow, and a recipient of many international awards and honors including Doctor Honoris Causa degrees from six universities over the world. He is a Highly Cited Researcher in Mathematics. His research has been supported by continued grants from the National Science Foundations and the Air Force Office of Scientific Research.

Nguyen Mau Nam, PhD, is Professor of Mathematics at Portland State University. He has published more than 60 research articles and one book in convex analysis with applications to optimization theory and numerical algorithms. He has received several awards for his research including a best paper award by Journal of Global Optimization in 2021 and the Columbia-Willamette Chapter of Sigma Xi Outstanding Researcher Award in Mathematical Sciences in 2015. His research was supported by grants from the National Science Foundation, the Simons Foundation, and Portland State University.