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

Yanqin  Bai; Pengfei  Ma; Jing  Zhang

doi:10.3934/jimo.2016.12.739

Article Contents

2016, Volume 12, Issue 2: 739-756. Doi: 10.3934/jimo.2016.12.739

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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

Received: April 30, 2014

Revised: February 28, 2015

Published: March 2016

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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 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].

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Mathematics Subject Classification: Primary: 90C25, 90C51; Secondary: 90C60.

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