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April  2016, 12(2): 739-756. doi: 10.3934/jimo.2016.12.739

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

 1 Department of Mathematics, Shanghai University, Shanghai 200444 2 Department of Mathematics, Shanghai University, Shanghai, 200444, China, China

Received  May 2014 Revised  March 2015 Published  June 2015

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 of optimal 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 a kernel 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 is polynomial-time solvable. Finally we illustrate the performance of interior-point method by a real-world quadruped robot example of optimal contact forces taken from the literature [10].
Citation: Yanqin Bai, Pengfei Ma, Jing Zhang. A polynomial-time interior-point method for circular cone programming based on kernel functions. Journal of Industrial & Management Optimization, 2016, 12 (2) : 739-756. doi: 10.3934/jimo.2016.12.739
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