Argyros, G.Argyros, M.Argyros, I.K.George, S.2026-02-052021Communications on Applied Nonlinear Analysis, 2021, 28, 1, pp. 57-641074133Xhttps://idr.nitk.ac.in/handle/123456789/23446The convergence region of algorithm is not large in general, limiting the choice of starters. Moreover, the error distances are pessimistic. Motivated by optimization concerns and these draw backs, we develop a technique that locates a smaller than before set which also contains the iterates of the algorithm. The majorant functions connected to this set are more precise resulting to a finer convergence analysis than before but without more conditions. In particular, our technique is used to solve constrained nonlinear systems using an inexact Newton-Frank-Wolfe-Type-Algorithm (INFWTA). This technique is so general that it can be used to extend the usage of other algorithms along the same lines. © 2021, International Publications. All rights reserved.Constrained systemsFrank-Wolfe algorithmGradient methodLocal convergenceNewton-type method