A Derivative-free Method For Solving Nonsmooth Nonlinear Equations

Solving nonlinear equations is an important subject in numerical optimization.Nonlinear equations are closely related to many optimization problems,such as optimality conditions,variational inequalities,and nonlinear complementarity problems.In real life,nonlinear equations widely exist in the fields of national defense,aerospace,economy,engineering,management and so on.It is of theoretical and practical significance to explore new methods suitable for solving different kind of nonlinear equations.In this thesis,by studying subderivative and subdifferential properties of the merit function for the system of nonlinear equations,the calculation formulas of the subderivative,Clarke directional derivative,regular subdifferential,subderivative and Clarke subdifferential are given,and their KL properties are further analyzed.Finally,we establish a derivative-free descent algorithm with simple iteration format.Under mild assumptions,the merit function sequences Q-linearly converges to 0,and the sequences generated by our algorithm Rlinearly converges to a solution of the equation system.The algorithm has satisfactory performance in numerical experiments for solving nonlinear equations.