Fundamentals of Convex Analysis and Optimization

Rafael Correa, Mathematical Engineering Degree from the University of Chile (1971), Doctor in Engineering, University of Clermont, France (1974) and Doctor in Mathematics Science, Blaise Pascal University, France (1984). He served as Executive Director of CONICYT, the Chilean National Agency for Scientific Research and Development (1990-1994), as Founder and Director of the Mathematical Modeling Center (CMM) at the University of Chile (2000-2007), and as President of O’Higgins University Chile, since its foundation in 2015. Author of fifty papers on Mathematical Optimization and Variational Analysis.Abderrahim Hantoute, Doctor in Applied Mathematics from Université Paul Sabatier de Toulouse (2003), Postdoc Fellowship in Alicante and Elche Universities 2004-2007, Associate researcher (at CMM, Universidad de Chile until 2020, and then at Universidad de Alicante). According to MathSciNet: 47 papers, with 316 citations by 182authors.Marco A. López, Doctor in Mathematics from Valencia University (1973), Full Professor since 1981, currently at Alicante University as Emeritus Professor. Doctor Honoris Causa by the University of Limoges (2012), Honorary Adjunct Professor of Federation University, Australia (2013), as and Corresponding Member of the Real Academia de Ciencias of Spain (2014). Research on mathematical optimization, semi-infinite programming, variational analysis and game theory. According to MathSciNet: 151 papers, with 1788 citations by 590 authors.

• 1. Introduction.- 2. Preliminaries.- 3. Fenchel-Moreau-Rockafellar theory.- 4. Fundamental topics in convex analysis.- 5. Supremum of convex functions.- 6. The supremum in specific contexts.- 7.  Other subdifferential calculus rules.- 8. Miscellaneous.- 9. Exercises - Solutions.- Index.- Glossary of Notations.- Bibliography.

“Each chapter is provided with a bibliography and includes lots of examples and exercises with answers. There is also a brief introduction to convex analysis, Fenchel- Moreau-Rockafellar theory, and functional analysis in the book.” (Svetlana A. Kravchenko, zbMATH 1540.90195, 2024)