In the paper a primal-infeasible interior point algorithm is proposed for linearly constrained convex programming. The starting point is any positive primal-infeasible dual-feasible point in a large region. The method maintains positivity of the iterates which point satisfies primal-infeasible dual-feasible point. At each iterates it requires to solve approximately a nonlinear system. It is shown that, after polynomial iterations a sufficiently good approximation to the optimal point is found, or there is no optimal point in a large nonnegative region.
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