ON IMPLEMENTATION OF A SELF-DUAL EMBEDDING METHOD FOR CONVEX PROGRAMMING ∗ JOHNNY TAK WAI CHENG and SHUZHONG ZHANG † Department of Systems Engineering and Engineering Management, The Chinese University of Hong Kong, Shatin, Hong Kong (Received 15 October 2003; Revised 13 August 2004) In this paper, we implement Zhang’s method [22], which transforms a general convex optimization problem with smooth convex constraints into a convex conic optimization problem and then apply the techniques of self-dual embedding and central path following for solving the resulting conic op- timization model. A crucial advantage of the approach is that no initial solution is required, and the method is particularly suitable when the feasibility status of the problem is unknown. In our implementation, we use a merit function approach proposed by Andersen and Ye [1] to determine the step size along the search direction. We evaluate the efficiency of the proposed algorithm by observing its performance on some test problems, which include logarithmic functions, exponential functions and quadratic functions in the constraints. Furthermore, we consider in particular the geometric programming and L p -programming problems. Numerical results of our algorithm on these classes of optimization problems are reported. We conclude that the algorithm is stable, efficient and easy-to-use in general. As the method allows the user to freely select the initial solution if he/she so wishes, it is natural to take advantage of this and apply the so-called warm-start strategy, whenever the data of a new problem is not too much different from a previously solved problem. This strategy turns out to be effective, according to our numerical experience. Keywords: Convex programs; conic optimization; self-dual embedding; path-following. 2000 Mathematics Subject Classification codes: 90C25; 90C51; 65K05. * This research was supported by Hong Kong RGC Earmarked Grant CUHK4233/01E. † Corresponding author. E-mail: zhang@se.cuhk.edu.hk.