In this paper, we study continuity and Lipschitzian properties of set-valued mappings, focusing on inner-type conditions. We introduce new notions inner calmness* and, its relaxation, fuzzy calmness*. show that polyhedral maps enjoy examine (fuzzy) a multiplier mapping associated with constraint systems in depth. Then utilize these to develop some rules generalized differential calculus, mainly...

Let Lθ be the circular cone in IR which includes second-order cone as a special case. For any function f from IR to IR, one can define a corresponding vector-valued function fLθ on IR by applying f to the spectral values of the spectral decomposition of x ∈ IR with respect to Lθ. The main results of this paper are regarding the Hdifferentiability and calmness of circular cone function fLθ . Spe...

This study examined the relationship between exertion level and affect using the framework of opponent-process theory and the dual-mode model, with the Activation-Deactivation Adjective Checklist and the State Anxiety Inventory among 14 active and 14 sedentary participants doing 20 min of treadmill exercise at speeds of 5% below, 5% above, and at lactate threshold (LT). We found a significant e...

In this paper, we provide a complete characterization of the robust isolated calmness of the KarushKuhn-Tucker (KKT) solution mapping for convex constrained optimization problems regularized by the nuclear norm function. This study is motivated by the recent work in [8], where the authors show that under the Robinson constraint qualification at a local optimal solution, the KKT solution mapping...

Previous research using the model proposed by Davidson has shown that resting frontal electroencephalographic (EEG) asymmetry can predict affective responses to aerobic exercise at moderate intensities. Specifically, greater relative left frontal activity has been shown to predict positive affect (i.e., energy) following exercise. The purpose of this study was to determine if resting frontal EE...

Our paper deals with the interrelation of optimization methods and Lipschitz stability of multifunctions in arbitrary Banach spaces. Roughly speaking, we show that linear convergence of several first order methods and Lipschitz stability mean the same. Particularly, we characterize calmness and the Aubin property by uniformly (with respect to certain starting points) linear convergence of desce...

This paper is devoted to the development of new sufficient conditions for the calmness and the Aubin property of implicit multifunctions. As the basic tool we employ the directional limiting coderivative which, together with the graphical derivative, enables a fine analysis of the local behavior of the investigated multifunction along relevant directions. For verification of the calmness proper...