Relation between Demyanov difference and Minkowski difference of convex compact subsets inR 2

2007 ◽  
Vol 23 (1-2) ◽  
pp. 353-359
Author(s):  
Chun-Ling Song ◽  
Zun-Quan Xia ◽  
Li-Wei Zhang ◽  
Shu-Yang Li
Keyword(s):  
Convex Compact ◽  
Difference Of Convex ◽  
Minkowski Difference ◽  
Compact Subsets

scholarly journals A generalization of Kantorovich operators for convex compact subsets

2017 ◽  
Vol 11 (3) ◽  
pp. 591-614 ◽  
Author(s):  
Francesco Altomare ◽  
Mirella Cappelletti Montano ◽  
Vita Leonessa ◽  
Ioan Raşa
Keyword(s):  
Convex Compact ◽  
Kantorovich Operators ◽  
Compact Subsets

On regularization of right hand sides of differential relations

1984 ◽  
Vol 97 ◽  
pp. 151-159 ◽  
Author(s):  
Jaroslav Kurzweil ◽  
Jiří Jarník
Keyword(s):  
Banach Space ◽  
Separable Banach Space ◽  
Convex Compact ◽  
Regular Map ◽  
Upper Semicontinuous ◽  
Right Hand ◽  
Differential Relations ◽  
Compact Subsets

SynopsisLet the values of F be convex compact subsets of Rn and let F be upper semicontinuous with respect to x. There are two ways known of replacing F by a more regular map so that the set of solutions of (2) remains unchanged. We prove that both ways lead to the same more regular map and extend the results to the case where Rn is replaced by a separable Banach space.

scholarly journals An Efficient Method for Convex Constrained Rank Minimization Problems Based on DC Programming

2016 ◽  
Vol 2016 ◽  
pp. 1-13
Author(s):  
Wanping Yang ◽  
Jinkai Zhao ◽  
Fengmin Xu
Keyword(s):  
Objective Function ◽  
Minimization Problem ◽  
Dc Programming ◽  
Rank Minimization ◽  
Closed Form Solutions ◽  
Minimization Problems ◽  
Difference Of Convex Functions ◽  
Convex Objective Function ◽  
Difference Of Convex ◽  
Cut Problems

The constrained rank minimization problem has various applications in many fields including machine learning, control, and signal processing. In this paper, we consider the convex constrained rank minimization problem. By introducing a new variable and penalizing an equality constraint to objective function, we reformulate the convex objective function with a rank constraint as a difference of convex functions based on the closed-form solutions, which can be reformulated as DC programming. A stepwise linear approximative algorithm is provided for solving the reformulated model. The performance of our method is tested by applying it to affine rank minimization problems and max-cut problems. Numerical results demonstrate that the method is effective and of high recoverability and results on max-cut show that the method is feasible, which provides better lower bounds and lower rank solutions compared with improved approximation algorithm using semidefinite programming, and they are close to the results of the latest researches.

Smooth Time-Optimal Path Tracking for Robot Manipulators With Kinematic Constraints

2020 ◽  
Author(s):  
Kui Hu ◽  
Yunfei Dong ◽  
Dan Wu
Keyword(s):  
Robot Manipulators ◽  
Optimal Path ◽  
Path Tracking ◽  
Control Input ◽  
Kinematic Constraints ◽  
Computation Efficiency ◽  
Planning Approach ◽  
Time Optimal ◽  
Difference Of Convex ◽  
The Difference

Abstract Previous works solve the time-optimal path tracking problems considering piece-wise constant parametrization for the control input, which may lead to the discontinuous control trajectory. In this paper, a practical smooth minimum time trajectory planning approach for robot manipulators is proposed, which considers complete kinematic constraints including velocity, acceleration and jerk limits. The main contribution of this paper is that the control input is represented as the square root of a polynomial function, which reformulates the velocity and acceleration constraints into linear form and transforms the jerk constraints into the difference of convex form so that the time-optimal problem can be solved through sequential convex programming (SCP). The numerical results of a real 7-DoF manipulator show that the proposed approach can obtain very smooth velocity, acceleration and jerk trajectories with high computation efficiency.

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