A predictor-corrector algorithm combined conjugate gradient with homotopy interior point for general nonlinear programming

This paper transfers the general nonlinear programming problem with the equality and inequality constraints into the nonlinear programming problem with only inequality constraints to solve. Homotopy method is used to construct a conjugate gradient predictor-corrector tracking combined homotopy interior point algorithm. Finally, the global linear convergence of the algorithm is proved under the normal cone condition for the feasible region.