A New Sequential Systems of Linear Equations Algorithm of Feasible Descent for Inequality Constrained Optimization

Based on a new efficient identification technique of active constraints introduced in thispaper,a new sequential systems of linear equations (SSLE) algorithm generating feasible iterates isproposed for solving nonlinear optimization problems with inequality constraints.In this paper,we introducea new technique for constructing the system of linear equations,which recurs to a perturbationfor the gradients of the constraint functions.At each iteration of the new algorithm,a feasible descentdirection is obtained by solving only one system of linear equations without doing convex combination.To ensure the global convergence and avoid the Maratos effect,the algorithm needs to solve two additionalreduced systems of linear equations with the same coefficient matrix after finite iterations.Theproposed algorithm is proved to be globally and superlinearly convergent under some mild conditions.What distinguishes this algorithm from the previous feasible SSLE algorithms is that an improvingdirection is obtained easily and the computation cost of generating a new iterate is reduced.Finally,apreliminary implementation has been tested.