Convexity, Optimization and Approximation, with some Applications

The present book has didactic and scientific content. In the first two chapters (no.0 and 1), some basic results in convex analysis, optimization and approximation on finite dimensional spaces are recalled. Elements of integral representation and approximation on infinite dimensional spaces are briefly discussed as well. A few related results in functional analysis are applied. Chapter 2 is devoted to the classical theory of the Calculus of Variations. In chapter 3, Markov moment problem and its relationship with other fields is the main subject. The proofs are based on results in functional analysis. The second part of the book (chapters 4, 5 and 6) may be useful to any reader interested in multidimensional (scalar and multiobjective) optimization problems. Furthermore, the theoretical aspects developed in this part are illustrated with some real-life applications. Examples, exercises and/or applications are presented in each chapter of this book.