Lipschitz Behavior of Solutions to Convex Minimization Problems
Jean‐Pierre Aubin · Mathematics of Operations Research · 1984
We derive the Lipschitz dependence of the set of solutions of a convex minimization problem and its Lagrange multipliers upon the natural parameters from an inverse function theorem for set-valued maps. This requires the use of contingent and Clarke derivatives of set-valued maps, as well as generalized second derivatives of convex functions.