Optimization and differentiation in Banach spaces (Q1096138)

The author shows that some old ideas of Smulian can be used to give another proof of a theorem of Bourgain which characterizes RNP sets in terms of strongly exposed points. By means of optimization results, he gives a characterization theorem on RNP sets in real Banach spaces with a more concise proof than before. This theorem also shows that a converse of the main result in his earlier paper [Math. Ann. 236, 171-176 (1978; Zbl 0365.49006)] holds. Furthermore, some attempts to extend optimization results obtained in real Banach spaces to the case of complex ones have been made.