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Nonsmooth Quasiconcave Programming

Yoshihiro Tanaka (tanaka***at***econ.hokudai.ac.jp)

Abstract: 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.

Keywords: Arrow-Enthoven's sufficient optimality theorem, quasiconcave programming, locally Lipschitz, the Rawlsian social welfare function

Category 1: Convex and Nonsmooth Optimization (Generalized Convexity/Monoticity )

Citation: Discusion Paper Series A: No. 2006-166, Grad. School of Economics and Business Admin, Hokkaido University, Sapporo 060-0809, JAPAN, August/2006.

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Entry Submitted: 01/24/2007
Entry Accepted: 01/24/2007
Entry Last Modified: 02/12/2007

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