In this paper, the Iri-Imai algorithm for solving linear and convex quadratic programming is extended to solve some other smooth convex programming problems. The globally linear convergence rate of this extended algorithm is proved, under the condition that the objective and constraint functions satisfy a certain type of convexity, called the harmonic convexity in this paper. A characterization of this convexity condition is given. The same convexity condition was used by Mehrotra and Sun to prove the convergence of a path-following algorithm. The Iri-Imai algorithm is a natural generalization of the original Newton algorithm to constrained convex programming. Other known convergent interior-point algorithms for smooth convex programming are mainly based on the path-following approach.

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Journal of Optimization Theory and Applications
Erasmus School of Economics

Zhang, S. (1994). Convergence property of the Iri-Imai algorithm for some smooth convex programming problems. Journal of Optimization Theory and Applications, 82(1), 121–138. doi:10.1007/BF02191783