Nonsmooth Optimization Methods and Applications provides an overview of this branch of mathematics, concentrating on the interaction between the theory and its applications.

F. Giannessi, Department of Mathematics, University of Pisa, Italy.

Preface 1. Nonsmooth unilateral problems 2. On the sub different lability of functions of a matrix spectrum I: mathematical foundations 3. On the sub different lability of functions of a matrix spectrum II: subdifferential formulas 4. Evolution to selected nash equilibria 5. On a criterion for the existence of traces in kinetic theory 6. A new class of invex multifunctions 7. Discontinuous quasi-variational inequalities and applications to equilibrium problems 8. Calculus of Variations in nonsmooth presentation 9. On a general scheme for solving inclusions using derivatives of set-valued mappings 10. Regularity conditions and exact penalty functions in Lipschitz programming problems 11. Treatment of certain nonsmooth vector optimization problems via geometric vector optimization 12. Structural optimization techniques as a mathematical tool for finding optimal shapes of complex shell structures 13. Conical inverse mapping theorems and applications to some control problems 14. What conditions are satisfied at points minimizing the maximum of a finite number of differentiable functions? 15. A restricted step proximal bundle method for nonconvex nondifferentiable optimization 16. On generalized upper quasidifferentiability 17. Lagrangian decomposition and nonsmooth optimization: bundle algorithm, prox iteration, augmented Lagrangian 18. Best rational approximation on a system of intervals 19. Ideas for developing a rapidly convergent algorithm for nonsmooth minimization 20. On some noncoercive problems related to delamination in layered composites 21. Hemivariational inequalities. Applications to Mechanics and control problems 22. Some calculus rules for semidifferentiable functions and related topics 23. Some remarks on semistationarity and optimality conditions 24. Second-order generalized derivatives: relationships with convergence notions 25. Analytical and computational advances in quasi differential calculus for nonsmooth optimization 26. Amenable functions in optimization 28. Differences of convex compact sets and their applications in nonsmooth analysis 29. On some problems of nonsmooth optimization in economic theory 30. Generalized monotone maps 31. A new local characterization of pseudoconvex functions and their nonsmooth extensions 32. Some recent mean value theorems in nonsmooth analysis 33. On a new stability condition in mathematical programming