This paper is devoted to optimality conditions for nonsmooth quasiconcave programming. Arrow and Enthoven (1961) formulate several economic problems into quasiconcave programming, and give a sufficient condition for smooth quasiconcave programming in their epoch-making and comprehensive paper. In this paper, generalized necessary and sufficient conditions for nonsmooth quasiconcave programming have been derived in terms of the Clarke subdifferential (1990). A Slater-type constraint qualification is introduced to derive the generalized Kuhn-Tucker necessary condition effectively. An application to the Rawsian social welfare function is discussed.
Discusion Paper Series A: No. 2006-166, Grad. School of Economics and Business Admin, Hokkaido University, Sapporo 060-0809, JAPAN, August/2006.