Perturbed minimization principles and applications. (Q2760176)

Due to lack of compactness, lower semi-continuous and bounded below functionals on infinite dimensional Banach spaces do not attain their minimum in general. In order to establish several existence results, one is therefore bound to perturb the functional with a controlable function (which is usually ``smooth'' and ``small'') in such a way that the perturbed functional attains its minimum (and sometimes uniquely, or strongly).NEWLINENEWLINEThis very interesting survey, written by two main contributors to the field, gathers the most important perturbation principles, and a wealth of applications. Among these, let us mention in particular convergence of martingales and optimization on non-compact sets, the structure of Banach spaces which admit a separating polynomial, non-smooth calculus and Rolle's theorems, the mountain pass theorem, and viscosity solutions to Hamilton-Jacobi equations.NEWLINENEWLINEThis survey will serve as a perfect guide for anyone who intends to contribute to this field.NEWLINENEWLINEFor the entire collection see [Zbl 0970.46001].