In this paper we study the bilevel dynamic problem, which is a hierarchy of two dynamic optimization problems, where the constraint region of the upper level problem is determined implicitly by the solutions to the lower level optimal control problem. To obtain optimality conditions, we reformulate the bilevel dynamic problem as a single level optimal control problem that involves the value fun...

Let Γ := {x ∈ R | q(x) ∈ Θ}, where q : R → R is a twice continuously differentiable mapping, and Θ is a nonempty polyhedral convex set in R. In this paper, we first establish a formula for exactly computing the graphical derivative of the normal cone mapping NΓ : R ⇒ R, x 7→ NΓ(x), under the condition that Mq(x) := q(x) − Θ is metrically subregular at the reference point. Then, based on this fo...

This study explores the perspectives of expectant parents on influence a single antenatal class incorporating education childbirth physiology and relaxation techniques. The data for this qualitative descriptive were collected via in-depth interviews with six women three birth partners. An enhanced understanding formed ‘different way thinking’ about childbirth, ‘inspired motivated’ exertion lear...

Introduction: Coronary artery disease is the most common type of cardiovascular disease. Despite the increasing number of patients with coronary artery disease, the lived experiences of these patients have remained unknown. The purpose of the study was to understand the lived experiences of elderly patients with coronary artery disease. Methods: This qualitative research was conducted usin...

Background and Objectives: Marital infidelity can endanger the mental health of the victims and cause them to hate the cheating spouse; accordingly, it is necessary to identify and reinforce the factors that help relive this painful experience. Therefore, this study aimed to evaluate the effectiveness of spiritual-religious interventions on increasing the sense of calmness and forgiveness in wo...

The bilevel program is an optimization problem in which the constraint involves solutions to a parametric problem. It well known that value function reformulation provides equivalent single-level problem, but it results nonsmooth never satisfies usual qualification, such as Mangasarian–Fromovitz qualification (MFCQ). In this paper, we show even first order sufficient condition for metric subreg...

We consider a class of variational relation problems, depending on two parameters from metric spaces. The issue under investigation is the behaviour solution in neighborhood fixed pair parameters, more precisely, H?lder calmness mapping. After establishing some sufficient condition for general framework, we particularize result inclusion and an equilibrium problem.

Abstract The paper utilizes Hölder graphical derivatives for characterizing strong subregularity, isolated calmness and sharp minimum. As applications, we characterize in linear semi-infinite optimization minimizers of some penalty functions constrained optimization.