Pablo Pedregal  studied Mathematics at U. Complutense (1986) and received his PhD degree from the University of Minnesota at the end of 1989, under the guidance of D. Kinderlehrer. In 1990 he became associate professor at U. Complutense. During the academic year 1994-95 he moved to the young U. de Castilla-La Mancha, and in 1997 he won a full professorship. His field of interest focuses on variational techniques applied to optimization in a broad sense, including, but not limited to, calculus of variations -especially vector, non convex problems, optimal design in continuous media, optimal control, etc, and more recently he has explored variational ideas in areas like controllability, inverse problems, PDEs, and dynamical systems. Since his doctorate, he has regularly traveled to research centers in the USA and Europe. He has written more than one hundred research articles, and several specialized books.

1 Overview. Part I Mathematical Programming. - 2 Linear Programming.- 3 Nonlinear programming.- 4 Numerical approximation.- Part II Variational problems.- 5 Basic theory for variational problems 6 Numerical approximation of variational problems.- Part III Optimal Control.- 7 Basic facts about optimal control . 8 Numerical approximation of basic optimal control problems, and dynamic programming. Part IV Appendix.- 9 Hints and solutions to exercises.

This book provides a basic, initial resource, introducing science and engineering students to the field of optimization. It covers three main areas: mathematical programming, calculus of variations and optimal control, highlighting the ideas and concepts and offering insights into the importance of optimality conditions in each area. It also systematically presents affordable approximation methods. Exercises at various levels have been included to support the learning process.