Glasnik Matematicki, Vol. 32, No.1 (1997), 153-165.
DUALITY IN MULTIPLE OBJECTIVE PROGRAMMING
INVOLVING SEMILOCALLY PREINVEX AND RELATED FUNCTIONS
Vasile Preda and I. M. Stancu-Minasian
University of Bucharest, Mathematics Faculty, 14 Academiei Street,
Bucharest, Romania
The Romanian Academy, Centre of Math. Statistics, Calea 13
Septembrie Nr. 13, 76100 Bucharest 5, Romania
Abstract. A nonlinear multiple objective programming
problem is considered where functions involved are
-semidifferentiable.
By consireding the concept of weak minima, the Fritz John type
and Karush-Kuhn-Tucker type necessary optimality conditions
are obtained. Moreover, a result relative to sufficiency of
optimality conditions is given. Wolfe and Mond-Weir type duality
results are given in terms of the
-semidifferentials
of the functions. The duality results are given using concepts
of generalized semilocally preinvex functions.
1991 Mathematics Subject Classification.
90C26, 90C29, 90C30, 49J52.
Key words and phrases. Multiple objective programming,
weak minimum, optimality conditions, duality, generalized preinvex
functions.
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