The development of new technologies has confronted the entire domain of science and industry with issues of big data's scalability as well as its integration with the purpose of forecasting analytics in its life cycle. In predictive analytics, the forecast of near-future and recent past - or in other words, the now-casting - is the continuous study of real-time events and constantly updated whe...

The analysis of the connections among generalized systems, Vector Optimization Problems and Variational Inequalities allows to deepen the study of the properties of the Minty Vector Variational Inequality. In particular, under suitable regularity assumptions,the equivalence between Minty Vector Variational Inequality and Stampacchia Vector Variational Inequality is shown.

Variational analysis has been recognized as a rapidly growing and fruitful area in mathematics concerning mainly the study of optimization and equilibrium problems, while also applying perturbation ideas and variational principles to a broad class of problems and situations that may be not of a variational nature. It can be viewed as a modern outgrowth of the classical calculus of variations, o...

This paper sheds new light on several interrelated topics of second-order variational analysis, both in finite and infinite-dimensional settings. We establish new relationships between second-order growth conditions on functions, the basic properties of metric regularity and subregularity of the limiting subdifferential, tilt-stability of local minimizers, and positive-definiteness/semidefinite...

In this paper directionally contextual concepts of variational analysis, based on dual-~pace cou-siructions similar to those in [4, 5], are introduced and studied. As an illustration of their usefulnes~, necessary and ft!so sufficient optimality conditions in terms of directioual subdiffeJ • ent.ials are established , and it is shown that they can be effective in the situations where known opti...

Using variational analysis, we study the linear regularity for a collection of finitely many closed sets. In particular, we extend duality characterizations of the linear regularity for a collection of finitely many closed convex sets to the possibly nonconvex setting. Moreover the sharpest linear regularity constant can also be dually represented under the subsmoothness assumption.

We develop an approach of variational analysis and generalized differentiation to conditioning issues for two-person zero-sum matrix games. Our major results establish precise relationships between a certain condition measure of the smoothing first-order algorithm proposed in [4] and the exact bound of metric regularity for an associated set-valued mapping. In this way we compute the aforementi...

1 Department of Mathematics, Nanjing University, Nanjing 210093, China 2 Department of Mathematics, University of Central Florida, Orlando, FL 32816, USA 3 Mathematics Department, COMSATS Institute of Information Technology, Islamabad, Pakistan 4 Department of Applied Mathematics, National Sun Yat-Sen University, Kaohsiung 804, Taiwan 5 School of Mathematics and LPMC, Nankai University, Tianjin...

we introduce variational inequality problems on hilbert $c^*$-modules and we prove several existence results for variational inequalities defined on closed convex sets. then relation between variational inequalities, $c^*$-valued metric projection and fixed point theory  on  hilbert $c^*$-modules is studied.