Secant-inexact projection algorithms for solving a new class of constrained mixed generalized equations problems

In this paper, a new version of a secant-type method for solving constrained mixed general-ized equations is addressed. The method is a combination of the secant method applied to generalized equations with the conditional gradient method. We use the contraction mapping principle to establish the convergence results. Moreover, by assuming the Lipschitz condition on the gradient and the metric regularity property, we show that the sequence generated by the proposed algorithm is well-defined and locally convergent for a solution with linear or superlinear rate.