Abstract
This paper revisits the well-known family of sequential convex programming methods. We adopt the difference of convex programming technique to relax a wide variety of nonconvex optimization problems into convex programs. We extend this approach to a sequential convex programming algorithm that can generate a convergent sequence of feasible points whose objective values monotonically improve. As an improvement upon the existing sequential methods, we prove that under certain assumptions, the proposed algorithm reaches feasibility within a finite number of rounds, as opposed to asymptotic feasibility. The effectiveness of the proposed approach is corroborated through experiments on the problem of robust linear regression.
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