Algorithms For Generalized Circular Cone Complementarity Problem

The generalized circular cone complementarity problem is a class of nonsymmetric cone optimization problems,which includes many circular cone optimization problems as special cases,such as linear circular cone programming,convex quadratic circular cone programming and circular cone complementarity problem.Circular cone programming and circular cone complementarity problem have been widely used in engineering problems,such as force optimization for the legs of a quadruped robot,the optimal grasping manipulation for multi-fingered robots,the optimal feet forces' distribution and the control of quadruped robots.In recent years,the circular cone optimization problem has received much attention,but it has many difficulties because the circular cone is nonsymmetric.By reading a lot of literatures and materials and mastering circular cone optimization problem theories and algorithms,this paper mainly studies the smoothingtype algorithm for solving the generalized circular cone complementary problem.The obtained results are listed as follows:1.We study a derivative-free smoothing algorithm for solving the general circular cone complementarity problem.By using a smoothing function,we reformulate the general circular cone complementarity problem as a system of smooth equations and solve it by Newton method.The algorithm adopts a new nonmonotone derivative-free line search and it has global and local quadratic convergence under some suitable conditions.Numerical results show that the algorithm is very effective.2.We study a smoothing inexact Newton method for solving the general circular cone complementarity problem.Based on a new smoothing function,we reformulate the general circular cone complementarity problem as a system of smooth nonlinear equations and propose an inexact Newton method to solve it.In each iteration,the proposed method solves the nonlinear equations only approximately and hence it is suitable to solve large scale general circular cone complementarity problems.Under suitable conditions,we prove that the proposed method has global and local quadratic convergence.Numerical results show that our algorithm is very effective.