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.

Automated summary

This paper discusses a new version of a secant-type method for solving constrained mixed generalized equations. The method combines the secant method with the conditional gradient method to achieve convergence of the solution. By assuming Lipschitz condition on the gradient and the metric regularity property, and using the contraction mapping principle, it is shown that the sequence generated by the proposed algorithm is well-defined and locally convergent with a linear or superlinear rate for the solution.