On the exact $$l_{1}$$ penalty function method for convex nonsmooth optimization problems with fuzzy objective function

Abstract

AbstractIn this paper, the convex nonsmooth optimization problem with fuzzy objective function and both inequality and equality constraints is considered. The Karush–Kuhn–Tucker necessary optimality conditions are proved for such a nonsmooth extremum problem. Further, the exact $$l_{1}$$ l 1 penalty function method is used for solving the considered nonsmooth fuzzy optimization problem. Therefore, its associated fuzzy penalized optimization problem is constructed in this approach. Then, the exactness property of the exact $$l_{1}$$ l 1 penalty function method is analyzed if it is used for solving the considered nonsmooth convex fuzzy optimization problem.