SUBDIFFERENTIAL PROPERTIES OF QUASI-CONVEX AND PSEUDOCONVEX FUNCTIONS- UNIFIED APPROACH

In this paper, we are mainly concerned with the characterization of qu asiconvex or pseudoconvex nondifferentiabIe functions and the relation ship between those two concepts. In particular, we characterize the qu asiconvexity and pseudoconvexity of a function by mixed properties com bining properties of the function and properties of its subdifferentia l. We also prove that a lower semicontinuous and radially continuous f unction is pseudoconvex if it is quasiconvex and satisfies the followi ng optimality condition: O epsilon partial derivative f(x)-->f has a g lobal minimum at x. The results are proved using the abstract subdiffe rential introduced in Ref. 1, a concept which allows one to recover al most all the subdifferentials used in nonsmooth analysis.