A polynomial-time interior-point method for circular cone programming based on kernel functions

Abstract

We present an interior-point method based on kernel functions for circular cone optimization problems, which has been found useful for describing optimal design problems ofoptimal grasping manipulation for multi-fingered robots. Since the well-known second order cone is a particular circular cone, we first establish an invertible linear mapping between a circular cone and its corresponding second order cone. Then we develop akernel function based interior-point method to solve circular cone optimization in terms of the corresponding second order cone optimization problem.We derive the complexity bound of the interior-point method and conclude that circular cone optimization ispolynomial-time solvable. Finally we illustrate the performance of interior-point method bya real-world quadruped robot example of optimal contact forces taken from the literature [10].