Modeling and Convexity

Convexity is a central concept in Applied Sciences and Engineering. It is central to the mathematical formalization of many physical phenomena and a large number of numerical procedures depend upon it. For example, convex analysis tools are involved in the modeling of mechanical systems containing unilateral constraints (contact, friction, plasticity, etc.), in the definition of constitutive relations of materials, and in variational and optimization methods.
This reference work gives the reader a complete and comprehensive presentation of the foundations of convex analysis and includes applications of practical significance and importance in engineering. The presentation of the theory is self-contained and 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.