en Other Other پژوهشی Original Sequential optimality conditions provide adequate theoretical tools to justify stopping criteria for nonlinear programming solvers. Here, nonsmooth approximate gradient projection and complementary approximate Karush-Kuhn-Tucker conditions are presented. These sequential optimality conditions are satisfied by local minimizers of optimization problems independently of the fulfillment of constraint qualifications. It is proved that nonsmooth complementary approximate Karush-Kuhn-Tucker conditions are stronger than nonsmooth approximate gradient projection conditions. Sufficiency for differentiable generalized convex programming is established. Optimization problems, Necessary optimality conditions, Constraint qualification, Necessary optimality conditions, Nonsmooth analysis 15 28 http://iors.ir/journal/browse.php?a_code=A-10-534-1&slc_lang=en&sid=1 S. Ahmadi s-ahmady@sci.ui.ac.ir 00031947532846001289 00031947532846001289 Yes Department of Mathematics, University of Isfahan, Isfahan, Iran N. Movahedian n.movahedian@sci.ui.ac.ir 00031947532846001290 00031947532846001290 No Department of Mathematics, University of Isfahan, Isfahan, Iran