Interior-point methods for convex programming (Q1205507)

This work is concerned with a general class of convex programming problems that could be solved by interior point methods. It is assumed that the objective function and also the constraints are twice continuously differentiable convex functions and the logarithmic transformation of the opposite of the problem's functions is self- concordant in the relative interior of the feasible set. It is shown that self-concordance is equivalent to a modified relative Lipschitz condition, and the relative Lipschitz condition for the constraint functions implies the modified relative Lipschitz condition (or self-concordance) for the barrier function. The results include a complete complexity analysis for a ``zero-order'' path-following method that seems to be simpler than other known methods.