Algorithm of Sequential Systems of Linear Equations with Superlinear and Quadratical Convergence for General Constrained Optimization

Optimization problems with general equality and inequality constraints are discussed. By using the techuique of sequential systems of linear equations and generalized projection, a feasible descent algorithm is presented, at each iteration of the algorithm, only one linear system and a generalized projection need to be solved and computed. Under suitable assumptions, the algorithm is proved to converge superlinearly and quadratically to a KT point of the problem. 