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SIAM Journal on Control and Optimization, Vol.32, No.3, 591-611, 1994
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.