This reference book gives the reader a complete but comprehensive
presentation of the foundations of convex analysis and presents
applications to significant situations in engineering. The presentation
of the theory is self-contained and the proof of all the essential
results is given. The examples consider meaningful situations such as
the modeling of curvilinear structures, the motion of a mass of people
or the solidification of a material. Non convex situations are
considered by means of relaxation methods and the connections between
probability and convexity are explored and exploited in order to
generate numerical algorithms.