On Second-Order Optimality Conditions for Vector Optimization

Necessary conditions for weak efficiency for nonsmooth degenerate multiobjective optimization problems

“…None of the results in [7,23,32,33] apply to this example as f 1 , g 1 and g 2 are not twice (continuously) differentiable nearx or even differentiable nearx. In particular, the primal second-order necessary conditions of Theorem 3.3 and of Theorem 4.1, [23], and of Corollary 3.1 and of Theorem 4.1, [7] are not applicable.…”

“…Theorem 4 extends to locally Lipschitz multiobjective optimization problems with inequality constraints and degenerate equality constraints our primal second-order necessary conditions of Theorem 2, [14] for scalar locally Lipschitz optimization problems with only inequality constraints. Most of the existing optimality conditions for problems involving either regular or degenerate equality constraints require the equality constraint function to be once or more times continuously differentiable (see, for instance, [3,21,23,[29][30][31][32][33]39]). We require the equality constraint function to be three times Fréchet differentiable only at the local weak minimum.…”

Some properties of second-order contingent epiderivatives and its applications to vector equilibrium problems

“…Basing on the concepts of secondorder contingent sets, the second-order contingent epiderivatives of a single-valued map are E-mail address: suanalysis@gmail.com. established; see [1,2,3,5,6,7] and the references therein. It is known that the existence results of the generalized second-order contingent epiderivative has been studied; see [5] and the references therein.…”

“…It is known that the vector equilibrium problem provides a unified mathematical model including vector complementarity problems, vector saddle point problems, vector optimization problems and vector variational inequality problems as special cases. A large number of results for vector equilibrium problem have been investigated consists of existences of solutions, see, for instance, Marín and Sama [8] and optimality conditions, see, for instance, [1,2,3,4,5,6,7,9,10,11,12,13,14,15,16] and the references therein.…”

Second- and First-Order Optimality Conditions in Vector Optimization

“…Generalizations of Ban-Tal's SOCQ were applied by Penot [20], Jimenez and Novo [15]. Optimality conditions were also obtained by Maciel, Santos, Sottosanto [17] using two types SOCQ. All mentioned authors investigated twice differentiable problems or C 2 ones.…”