Second-Order Optimality Conditions for Nonconvex Set-Constrained Optimization Problems

Sufficient Second Order Optimality Conditions for C Multiobjective Optimization Problems

In this work, we use the notion of Approximate Hessian introduced by Jeyakumar and Luc [19], and a special scalarization to establish sufficient optimality conditions for constrained multiobjective optimization problems. Throughout this paper, the data are assumed to be of class C, but not necessarily of class C.

Optimality Conditions for Constrained Optimization Problems

Optimality and Complexity for Constrained Optimization Problems with Nonconvex Regularization

In this paper, we consider a class of constrained optimization problems where the feasible set is a general closed convex set and the objective function has a nonsmooth, nonconvex regularizer. Such regularizer includes widely used SCAD, MCP, logistic, fraction, hard thresholding and non-Lipschitz Lp penalties as special cases. Using the theory of the generalized directional derivative and the t...

Higher-order optimality conditions for weakly efficient solutions in nonconvex set-valued optimization

Unfortunately, the incorrect version of [1, Theorem 4.3] was published. The correct version of [1, Theorem 4.3] is given in this paper. By employing the generalized higher-order contingent derivatives of set-valued maps, Wang et al. [1] established a sufficient optimality condition of weakly efficient solutions for (SV P): (SV P) min F(x), s.t. G(x) (−D) = ∅, x ∈ E. Theorem 1 (see [1, Theorem 4...

Optimality Conditions for Constrained Optimization