Subdifferential test for optimality
We provide a first-order necessary and sufficient condition for optimality of lower semicontinuous functions on Banach spaces using the concept of subdifferential. From the sufficient condition we derive that any subdifferential operator is monotone absorbing, hence maximal monotone when the function is convex.
subdifferential lower semicontinuity maximal monotonicity directional derivative first-order condition optimality criterion 49j52 49k27 26d10 26b25