This book contains a collection of exercises (called tapas) at undergraduate level, mainly from the fields of real analysis, calculus, matrices, convexity, and optimization. Most of the problems presented here are non-standard and some require broad knowledge of different mathematical subjects in order to be solved.
The book presents convex analysis as an advanced extension of standard calculus, emphasizing inequalities over equalities, making it suitable for graduate studies. It highlights minimization algorithms tailored for non-differentiable functions, showcasing applications in optimization and operations research. The work is divided into two parts: the first serves as an introductory textbook for courses or self-study, while the second delves into advanced topics for specialists, compiling previously unpublished results.
Advanced Theory and Bundle Methods
The book provides a detailed and accessible exploration of convex analysis, making it suitable for readers with little to no prior knowledge. It combines rigorous proofs with practical numerical calculations, supported by numerous examples and counter-examples to illustrate key concepts. The text is well-structured and visually engaging, appealing to both analysts and those new to the subject. Its clear geometric approach sets it apart from other works in the field, ensuring a comprehensive understanding for a diverse audience.