ON GENERALIZED 2ND-ORDER DERIVATIVES AND TAYLOR EXPANSIONS IN NONSMOOTH OPTIMIZATION

A representation of Cominetti and Correa's generalized second-order directional derivative [SIAM J. Control Optim., 28 (1990), pp. 789-8091 is given and then applied to obtain a Taylor theorem type result. A conjecture in [SIAM J. Control Optim, 28 (1990), pp. 789-8091 concerning functions of the form max1 less-than-or-equal-to i less-than-or-equal-to n g(i)(x) is proved under a strengthened assumption, but not true otherwise.