Optimality conditions for invex nonsmooth optimization problems with fuzzy objective functions
本文针对局部Lipschitz模糊函数定义了Clarke广义方向α-导数和广义梯度，并建立了带不等式与等式约束的非光滑模糊优化问题的Karush-Kuhn-Tucker最优性条件，通过构造双目标优化问题及其加权标量化问题来刻画弱非支配解。
Abstract In this paper, the definitions of Clarke generalized directional $$\alpha $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>α</mml:mi> </mml:math> -derivative and Clarke generalized gradient are introduced for a locally Lipschitz fuzzy function. Further, a nonconvex nonsmooth optimization problem with fuzzy objective function and both inequality and equality constraints is considered. The Karush-Kuhn-Tucker optimality conditions are established for such a nonsmooth extremum problem. For proving these conditions, the approach is used in which, for the considered nonsmooth fuzzy optimization problem, its associated bi-objective optimization problem is constructed. The bi-objective optimization problem is solved by its associated scalarized problem constructed in the weighting method. Then, under invexity hypotheses, (weakly) nondominated solutions in the considered nonsmooth fuzzy minimization problem are characterized through Pareto solutions in its associated bi-objective optimization problem and Karush-Kuhn-Tucker points of the weighting problem.