We provide a proximal average with repect to $1$-coercive Legendre function. In the sense of Bregman distance, envelope is convex combination envelopes individual functions. The mapping convexified mappings Techniques from variational analysis keys for average.

In this paper, we introduce and analyze some generalized hybrid proximal point algorithms for finding a common element of the set of zeros of a maximal monotone operator and the set of fixed points of a nonexpansive mapping in a Hilbert space. These algorithms include the previously known proximal point algorithms as special cases. Weak and strong convergence of the proposed proximal point algo...

We study stability properties of a proximal point algorithm for solving the inclusion 0 ∈ T (x) when T is a set-valued mapping that is not necessarily monotone. More precisely we show that the convergence of our algorithm is uniform, in the sense that it is stable under small perturbations whenever the set-valued mapping T is metrically regular at a given solution. We present also an inexact pr...

Minerals control many soil functions and play a crucial role in addressing global existential issues. Measuring the abundance of minerals is laborious, costly, time-consuming task; however, spectroscopy can be useful tool to overcome this issue. This work aimed map major mineralogical components soils Brazil from surface 1 m deep at spatial resolution 30 m. Spectral data Brazilian Soil Library ...

Obtaining knowledge about the distribution of spatial variability soil properties is crucial to proper site-specific management. One way improve quality mapping by using auxiliary information (covariate). The objective this study was test whether remote and proximal sensing data can assist in through geostatistical prediction. We worked an experimental area cultivated with sugarcane located Sao...

We study inexact proximal Newton-type methods to solve convex optimization problems in composite form: minimize x∈Rn f(x) := g(x) + h(x), where g is convex and continuously differentiable and h : R → R is a convex but not necessarily differentiable function whose proximal mapping can be evaluated efficiently. Proximal Newton-type methods require the solution of subproblems to obtain the search ...

In this paper, we introduce and study a system of mixed variational-like inclusions and a system of proximal operator equations in Banach spaces which contains variational inequalities, variational inclusions, resolvent equations, system of variational inequalities and system of variational inclusions in the literature as special cases. It is established that the system of mixed variational-lik...

A modified Gauss-type Proximal Point Algorithm (modified GG-PPA) is presented in this paper for solving the generalized equations like 0 ∈ T(x), where T a set-valued mapping acts between two different Banach spaces X and Y. By considering some necessary assumptions, we show existence of any sequence generated by GG-PPA prove semi-local local convergence results using metrically regular mapping....