In this paper, we present a nonmonotone smoothing Newton algorithm for solving the circular cone programming(CCP) problem in which a linear function is minimized or maximized over the intersection of an affine space w...In this paper, we present a nonmonotone smoothing Newton algorithm for solving the circular cone programming(CCP) problem in which a linear function is minimized or maximized over the intersection of an affine space with the circular cone. Based on the relationship between the circular cone and the second-order cone(SOC), we reformulate the CCP problem as the second-order cone problem(SOCP). By extending the nonmonotone line search for unconstrained optimization to the CCP, a nonmonotone smoothing Newton method is proposed for solving the CCP. Under suitable assumptions, the proposed algorithm is shown to be globally and locally quadratically convergent. Some preliminary numerical results indicate the effectiveness of the proposed algorithm for solving the CCP.展开更多
In this paper,we consider an optimization problem of the grasping manipulation of multi-fingered hand-arm robots.We first formulate an optimization model for the problem,based on the dynamic equations of the object a...In this paper,we consider an optimization problem of the grasping manipulation of multi-fingered hand-arm robots.We first formulate an optimization model for the problem,based on the dynamic equations of the object and the friction constraints.Then,we reformulate the model as a convex quadratic programming over circular cones.Moreover,we propose a primal-dual interior-point algorithm based on the kernel function to solve this convex quadratic programming over circular cones.We derive both the convergence of the algorithm and the iteration bounds for largeand small-update methods,respectively.Finally,we carry out the numerical tests of 180◦and 90◦manipulations of the hand-arm robot to demonstrate the effectiveness of the proposed algorithm.展开更多
基金supported by the National Natural Science Foundation of China(11401126,71471140 and 11361018)Guangxi Natural Science Foundation(2016GXNSFBA380102 and 2014GXNSFFA118001)+2 种基金Guangxi Key Laboratory of Cryptography and Information Security(GCIS201618)Guangxi Key Laboratory of Automatic Detecting Technology and Instruments(YQ15112 and YQ16112)China
文摘In this paper, we present a nonmonotone smoothing Newton algorithm for solving the circular cone programming(CCP) problem in which a linear function is minimized or maximized over the intersection of an affine space with the circular cone. Based on the relationship between the circular cone and the second-order cone(SOC), we reformulate the CCP problem as the second-order cone problem(SOCP). By extending the nonmonotone line search for unconstrained optimization to the CCP, a nonmonotone smoothing Newton method is proposed for solving the CCP. Under suitable assumptions, the proposed algorithm is shown to be globally and locally quadratically convergent. Some preliminary numerical results indicate the effectiveness of the proposed algorithm for solving the CCP.
基金the National Natural Science Foundation of China(No.11371242)。
文摘In this paper,we consider an optimization problem of the grasping manipulation of multi-fingered hand-arm robots.We first formulate an optimization model for the problem,based on the dynamic equations of the object and the friction constraints.Then,we reformulate the model as a convex quadratic programming over circular cones.Moreover,we propose a primal-dual interior-point algorithm based on the kernel function to solve this convex quadratic programming over circular cones.We derive both the convergence of the algorithm and the iteration bounds for largeand small-update methods,respectively.Finally,we carry out the numerical tests of 180◦and 90◦manipulations of the hand-arm robot to demonstrate the effectiveness of the proposed algorithm.
