In this interesting monographical book infinite-dimensional analysis is used to study in a comprehensive way Lagrange multiplier approach to nonlinear variational problems with equality and (with help of cones) inequality constraints. The contents of the book can be characterized by three intimately connected points:

–

Existence of Lagrange multipliers and sensitivity analysis (including convex analysis),

–

Computational methods and their behaviour for different classes of the considered variational problems,

–

Profound examples, which fit in the framework of both the first points.

Just these examples, their treatment together with solution techniques, make the book suspenseful and exciting. One finds optimal control problems, structural optimization, inverse, contact, obstacle, Signorini and friction problems, image reconstruction, mathematical finance, problems with constraining partial differential equations, problems with free boundaries, elliptic, parabolic and Navier-Stokes equations. The book is clearly written, with full proofs and it is convenient, that it starts with a rich in content preface (of seven pages).