On some efficient interior point methods for nonlinear convex programming

AbstractWe introduce two interior point algorithms for minimizing a convex function subject to linear constraints. Our algorithms require the solution of a nonlinear system of equations at each step. We show that if sufficiently good approximations to the solutions of the nonlinear systems can be found, then the primal-dual gap becomes less that ε in O(n|lnε|) steps, where n is the number of variables