An extension of the proximal minimization algorithm is considered where only some of the minimization variables appear in the quadratic proximal term. The resulting iterates are interpreted in terms of the iterates of the standard algorithm, and a uniform descent property is shown that holds independently of the proximal terms used. This property is used to give simple convergence proofs of par...

We consider an extension of the proximal minimization algorithm where only some of the minimization variables appear in the quadratic proximal term. We interpret the resulting iterates in terms of the iterates of the standard algorithm and we show a uniform descent property, which holds independently of the proximal terms used. This property is used to give simple convergence proofs of parallel...

We introduce a generalized version of the concave Kurdyka-?ojasiewicz (KL) property by employing nonsmooth desingularizing functions. also present exact modulus KL property, which provides an answer to open question regarding optimal function. The is designed be smallest among all possible Examples are given illustrate this pleasant property. In turn, using modulus, we provide sharpest upper bo...

A subset X of a real Hilbert space H is said to be proximally smooth provided that the function d X : H ! R (the distance to X) is continuously diierentiable on an open tube U around X. It is proven that this property is equivalent to d X having a nonempty proximal subgradient at every point of U, and that the (G^ ateaux = Fr echet) derivative is locally Lipschitz on U. The Lipschitz behavior o...

In this article, we introduce a new class of non-self mappings, called weak proximal contractions, which contains the proximal contractions as a subclass. Existence and uniqueness results of a best proximity point for weak proximal contractions are obtained. Also, we provide sufficient conditions for the existence of common best proximity points for two non-self mappings in metric spaces having...

As a form of tenancy in common, heirs’ property presents numerous obstacles to owners’ ability to build wealth. This is because the titles for such properties are unclear or “clouded” and cannot be uses as collateral for loans. The bulk of the heirs’ property literature focuses on rural, African American landholdings in the Black Belt South, where the extent of heirships have been estimated to ...

central to vygotsky-inspired sociocultural theory (sct) is the notion of zpd seen by sla researchers as a useful framework within which l2 teaching and learning can take place. van lier (2004) argues that the zpd could be activated in diverse proximal contexts (pcs) and is not limited to the expert-novice scenario. . this study probed whether iranian efl learners' collaborative task performance...

We introduce a geometrically transparent strict saddle property for nonsmooth functions. This guarantees that simple proximal algorithms on weakly convex problems converge only to local minimizers, when randomly initialized. argue the may be realistic assumption in applications, since it provably holds generic semi-algebraic optimization problems.