This book is meant for master, graduate, and PhD students who need
to learn the basics of convex analysis, for use in some of the many applications
of convex analysis, such as, for example, machine learning, robust optimization,
and economics. Prerequisites to reading the book are: some familiarity with linear
algebra, the differential calculus, and Lagrange multipliers. The necessary background information can be found elsewhere in standard texts, often in appendices:
for example, pp. 503–527 and pp. 547–550 from the textbook [1] “Optimization:
Insights and Applications,” written jointly with Vladimir M. Tikhomirov.
Each chapter starts with an abstract (why and what),
a road map, a section providing motivation (optional), and it ends with a section
providing applications (optional), and many exercises (the more challenging ones
are marked by a star).