This monograph is devoted to the exposition of new ways of formulating problems of structural optimization with incomplete information and techniques of solution.?Research results concerning the optimum shape and structural properties of the bodies subjected to external loadings are recapitulated. Problems of optimal design with incomplete information, accounting for the interaction between the structure and its environment, properties of materials, existence of initial damages and damage accumulation are studied. This?volume?treats overcoming the corresponding mathematical difficulties caused by raising local functionals. Most of the book is devoted to the minimax approach using worst case scenarios,?i.e.?the so-called guaranteed approach.