In this note, we prove that the KKT mapping for nonlinear semidefinite optimization problem is upper Lipschitz continuous at the KKT point, under the second-order sufficient optimality conditions and the strict Robinson constraint qualification.

We give a necessary and sufficient condition for a difference of convex (DC, for short) functions, defined on a normed space, to be Lipschitz continuous. Our criterion relies on the intersection of the ε-subdifferentials of the involved functions.

In this paper, we prove the existence and uniqueness result of the reflected BSDE with two continuous barriers under monotonicity and general increasing condition on y, with Lipschitz condition on z.

Let Ω be a bounded domain in R with a Lipschitz continuous boundary ∂Ω and outward unit normal vector n. We consider the following quasi-static Maxwell’s system with a nonlocal field-dependent source term,

Usually, given a continuous-time nonlinear model, a closed form solution for an exact discretization can not be found explicitly, originating the need of approximating discrete-time models. This note studies the preservation of the Lipschitz continuity under approximate discretizations.

Liu process is a type of fuzzy process. It is a fuzzy counterpart of Brownian motion. In this paper, the continuity property of Liu process is studied. It is proved that almost all Liu paths are Lipschitz continuous.