Ricerc@Sapienza

We consider nested variational inequalities consisting in a (upper-level) variational inequality whose feasible set is given by the solution set of another (lower-level) variational inequality. Purely hierarchical convex bilevel optimization problems and certain multi-follower games are particular instances of nested variational inequalities. We present an explicit and ready-to-implement Tikhonov-type solution method for such problems. We give conditions that guarantee the convergence of the proposed method.

When a genetic algorithm (GA) is employed in a statistical problem, the result is affected by both variability due to sampling and the

This is a companion paper to “Ghost penalties in nonconvex constrained
optimization: Diminishing stepsizes and iteration complexity" (to appear in Mathematics of
Operations Research). We consider the ghost penalty scheme for nonconvex, constrained
optimization introduced in that paper, coupled with a diminishing stepsize procedure. Under
an extended Mangasarian-Fromovitz-type constraint qualification we give an expression for
the maximum number of iterations needed to achieve a given solution accuracy according to