in this paper, using clarke’s generalized directional derivative and di-invexity we introduce new concepts of nonsmooth k-α-di-invex and generalized type i univex functions over cones for a nonsmooth vector optimization problem with cone constraints. we obtain some sufficient optimality conditions and mond-weir type duality results under the foresaid generalized invexity and type i cone-univexi...

This paper considers the optimal induced L2gain estimator design problem for infinite dimensional systems with finite dimensional outputs. It is shown that this problem is equivalent to a dual regulator design problem. Moreover the relationship between the dual problem and a two player differential game is established. A solution to the latter problem is derived which, in turn solves the dual r...

Background Phase contrast MRI has limited practical value in clinical applications due to its inherently long scan times [Kilner,JCMR’07]. Parallel imaging[Pruessmann, MRM’01] and spatio-temporal constrained reconstruction techniques[Tsao,MRM’03] have been shown beneficial[Baltes,MRM’05]. Dual slice approaches have shown advantages as compared to standard SENSE when multiple and sufficiently se...

We introduce a new g-frame (singleton g-frame), g-orthonormal basis and g-Riesz basis and study corresponding notions in some other generalizations of frames.Also, we investigate duality  for some kinds of g-frames. Finally, we illustrate an example which provides a  suitable translation from discrete frames to Sun's g-frames.

In the previous lecture, in the first place, we talked about duality for general non-convex optimization. And we know that dual functions are always convex. The dual of the dual problem is also convex. In applications, the dual of the dual can be used as the convex relaxation of the primal (and we will see this explicitly in the next lecture). Then, we covered the concepts of weak duality and s...

In mathematical programming, constraint qualifications are essential elements for duality theory. Recently, necessary and sufficient constraint qualifications for Lagrange duality results have been investigated. Also, surrogate duality enables one to replace the problem by a simpler one in which the constraint function is a scalar one. However, as far as we know, a necessary and sufficient cons...

$Rsb{0}$-algebras, which were proved to be equivalent to Esteva and Godo's NM-algebras modelled by Fodor's nilpotent minimum t-norm, are the equivalent algebraic semantics of the left-continuous t-norm based fuzzy logic firstly introduced by Guo-jun Wang in the mid 1990s.In this paper, we first establish a Stone duality for the category of MV-skeletons of $Rsb{0}$-algebras and the category of t...