A characterization of tyhonov well-posedness for minimum problems, with applications to variational inequalities(∗)
Roberto Lucchetti, Fioravante Patrone · Numerical Functional Analysis and Optimization · 1981
We give a characterization of Tyhonov well-posedness for the problem of minimising a convex lower-semieontinuous function f on a closed convex set K. To get this result, we use Ekeland's theorem on the“approximate variational principle”[21; when f is differentiable, the condition is and diam, where . We prove also some results relating the diameter of level sets of a sub- homogeneous function g with a function which characterizes the minimum increase of g above the minimum value. This result allows us to relate our characterization with a former one due to Zolezzi [10] Then we use the condition on diam(T∊) to give a definition of“well-posedness”for variational inequalities and prove some related results.