Exact Second-Order Cone Programming Relaxations for Some Nonconvex Minimax Quadratic Optimization Problems

2018 ◽  
Vol 28 (1) ◽  
pp. 760-787 ◽  
Author(s):  
V. Jeyakumar ◽  
G. Li
Keyword(s):  
Optimization Problems ◽  
Quadratic Optimization ◽  
Second Order ◽  
Cone Programming ◽  
Second Order Cone Programming ◽  
Second Order Cone

A new projection neural network for linear and convex quadratic second-order cone programming

2021 ◽  
pp. 1-13
Author(s):  
Yaling Zhang ◽  
Hongwei Liu
Keyword(s):  
Neural Network ◽  
Lyapunov Function ◽  
Optimization Problems ◽  
Second Order ◽  
Cone Programming ◽  
Second Order Cone Programming ◽  
Force Optimization ◽  
Second Order Cone ◽  
Grasping Force ◽  
Projection Neural Network

A new projection neural network approach is presented for the linear and convex quadratic second-order cone programming. In the method, the optimal conditions of the linear and convex second-order cone programming are equivalent to the cone projection equations. A Lyapunov function is given based on the G-norm distance function. Based on the cone projection function, the descent direction of Lyapunov function is used to design the new projection neural network. For the proposed neural network, we give the Lyapunov stability analysis and prove the global convergence. Finally, some numerical examples and two kinds of grasping force optimization problems are used to test the efficiency of the proposed neural network. The simulation results show that the proposed neural network is efficient for solving some linear and convex quadratic second-order cone programming problems. Especially, the proposed neural network can overcome the oscillating trajectory of the exist projection neural network for some linear second-order cone programming examples and the min-max grasping force optimization problem.

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