A sequential log barrier method for solving convex-concave problems with applications in robotics

In this paper we present a novel method to solve a convex-concave optimization problem. For this class of problems, several methods have already been developed. Sequential convex programming (SCP) is one of the state-of-the-art methods and involves solving a sequence of convex subproblems by linearizing the concave parts. These convex problems are e.g. solved by a log barrier method which solves a sequence of log barrier problems. To reduce the computational load we propose a sequential convex log barrier (SCLB) method where the main difference with SCP is that we search for an approximated solution of the convex subproblems by only solving one log barrier problem. We prove convergence of the proposed algorithm and we give some numerical examples that illustrate the decrease in computational load and similar convergence behaviour for a practical robotics application.