EVALUATION OF CLARKE'S GENERALIZED GRADIENT IN OPTIMIZATION OF VARIATIONAL INEQUALITIES
Tomáš Roubı́ček · Czech digital mathematics library · 1989
Optimization of systems governed by variational inequalities with linear constraints in IR" yields nonsmooth cost functions to be minimized.After discussion about various numerical methods to solve such optimization problems, we propose usage of a bundle or a subgradient algorithm and deal with the only problem how to evaluate in such case the generalized gradient of Clarke, required by it.As the problem in general is very complicated, an effective procedure is proposed only for certain special data.However, using the transversality theory, it is shown that "almost all" (possibly in the generic sense) sufficiently smooth data fulfil the conditions that guarantee the validity of the procedure proposed.