Javad Shaker Ardakani - Department of Mathematics‎, ‎Payame Noor University (PNU)‎, ‎P.OBox‎, ‎۱۹۳۹۵-۴۶۷۹‎, ‎Tehran‎, ‎Iran.
shahriar Farahmand Rad - Department of Mathematics‎, ‎Payame Noor University (PNU)‎, ‎P.OBox‎, ‎۱۹۳۹۵-۴۶۷۹‎, ‎Tehran‎, ‎Iran.
Nader Kanzi - Department of Mathematics‎, ‎Payame Noor University (PNU)‎, ‎P.OBox‎, ‎۱۹۳۹۵-۴۶۷۹‎, ‎Tehran‎, ‎Iran.

This paper studies the convex multiobjective optimization problem with vanishing constraints‎. ‎We introduce a new constraint qualification for these problems‎, ‎and then a necessary optimality condition for properly efficient solutions is presented‎. ‎Finally by imposing some assumptions‎, ‎we show that our necessary condition is also sufficient for proper efficiency‎. ‎Our results are formulated in terms of convex subdifferential.

Multiobjective optimization‎, ‎Vanishing constraints‎, ‎Convex optimization‎, ‎Constraint qualification