We consider the optimal value reformulation of the bilevel programming problem. It is shown that the Mangasarian-Fromowitz constraint qualification in terms of the basic generalized differentiation constructions of Mordukhovich, which is weaker than the one in terms of Clarke’s nonsmooth tools, fails without any restrictive assumption. Some weakened forms of this constraint qualification are th...

We study a general multiobjective optimization problem with variational inequality, equality, inequality and abstract constraints. Fritz John type necessary optimality conditions involving Mordukhovich coderivatives are derived. They lead to Kuhn-Tucker type necessary optimality conditions under additional constraint qualifications including the calmness condition, the error bound constraint qu...

We propose a new concept of generalized di erentiation of setvalued maps that captures rst order information. This concept encompasses the standard notions of Fréchet di erentiability, strict di erentiability, calmness and Lipschitz continuity in single-valued maps, and the Aubin property and Lipschitz continuity in set-valued maps. We present calculus rules, sharpen the relationship between th...

The purpose of this study was to observe and analyze the consumer behaviors and commentary of the Black Friday customer. An observational instrument documented consumer in-line behavior while waiting for the stores to open, store entry behavior, and individual behavior. Findings show that the majority of the shoppers demonstrated calmness, courteousness, and happiness during the shopping experi...

PURPOSE The purpose of this study was to evaluate the effects of Immersive Visualization (IV) eyewear on anxious, adult patients during oral debridement. METHODS Thirty adult volunteers (n=23 females; n=7 males) were enrolled in the study. Participants were required to be 18 years or older, exhibit at least moderate anxiety (score 9 or higher) on the Corah's Dental Anxiety Scale-Revised (DAS-...

The tiger image has become an integral part of world art and literature. No artists poets could remain indifferent to its regal appearance gracious movements, deceptive calmness sudden transformation into a vicious predator; they devoted their works this animal.
 Using rare matters connected with superstitions folklore Vietnam, the author observes relations human determines place in spirit...

Metric subregularity (respectively calmness) of multifunctions is a property which is not stable under smooth perturbations, implying that metric subregularity cannot be fully characterized by first order theory. In this paper we derive second order conditions for metric subregularity, both sufficient and necessary, for multifunctions associated with constraint systems as they occur in optimiza...