Miscellaneous incidences of convergence theories in optimization and nonlinear analysis I: Behavior of solutions

We examine some connections between convergence theories and optimization. In particular we study the Lipschitzian character of the infimal value function with respect to variations of the objective function. We also study the approximate solution multifunction for convex and nonconvex objective functions.Dedicated to the many real and putative authors of La Marseillaise, on its bicentennial.