A combined homotopy interior point method for convex nonlinear programming

In this paper, we present a new interior point method-combined homotopy interior point method (CHIP method) for convex nonlinear programming. Without strict convexity of the logarithmic barrier function and boundedness and nonemptiness of the solution set, we prove that for any epsilon > 0, an epsilon-solution of the problem can be obtained by the CHIP method. To our knowledge, strict convexity of the logarithmic barrier function and nonemptiness and boundedness of the solution set are the essential assumptions of the well-known center path-following method. Therefore, the CHIP method essentially reduces the assumptions of the center path-following method and can be applied to more general problems. (C) Elsevier Science Inc., 1997.