The bilevel program is an optimization problem in which the constraint involves solutions to
a parametric optimization problem. It is well known that the value function reformulation …

For bilevel programmes with a convex lower-level programme, the classical approach replaces
the lower-level programme with its Karush-Kuhn-Tucker condition and solve the resulting …

In this paper we study sufficient conditions for metric subregularity of a set-valued map which
is the sum of a single-valued continuous map and a locally closed subset. First we derive a …

In this paper, we study second-order necessary optimality conditions for smooth nonlinear
programming problems. Employing the second-order variational analysis and generalized …

Disrupted redox homeostasis contributes to renal ischemia–reperfusion (IR) injury. Abundant
natural products can activate nuclear factor erythroid-2-related factor 2 (Nrf2), thereby …

This paper is concerned with the directional derivative of the value function for a very general
set-constrained optimization problem under perturbation. Under reasonable assumptions, …

Grain size is an important trait influencing both the yield and quality of rice and its major
determinant is glume size. However, how glume size is regulated remains largely unknown. Here…

We consider a class of nonlinear delay lattices üi (t)+(− 1) p△ pui (t)+ λui (t)+ ui (t)= hi (ui (t−
ρ (t)))+ fi (t), i∈ Z, where λ is a real positive constant, p is any positive integer and△ is the …

The directional subdifferential of the value function gives an estimate on how much the optimal
value changes under a perturbation in a certain direction. In this paper we derive upper …

As a sister work of [Phys. Rev. D 79 (2009) 094004], we incorporate the color-screening
effect due to light quark pair creation into the heavy quark-antiquark potential, and investigate …