scholarly journals Z-type neural-dynamics for time-varying nonlinear optimization under a linear equality constraint with robot application

2018 ◽  
Vol 327 ◽  
pp. 155-166 ◽  
Author(s):  
Jian Li ◽  
Mingzhi Mao ◽  
Frank Uhlig ◽  
Yunong Zhang
Keyword(s):  
Nonlinear Optimization ◽  
Equality Constraint ◽  
Neural Dynamics ◽  
Time Varying ◽  
Linear Equality ◽  
Linear Equality Constraint

scholarly journals An efficient method for minimizing a convex separable logarithmic function subject to a convex inequality constraint or linear equality constraint

2006 ◽  
Vol 2006 ◽  
pp. 1-19 ◽  
Author(s):  
Stefan M. Stefanov
Keyword(s):  
Inequality Constraint ◽  
Point Of View ◽  
Equality Constraint ◽  
Polynomial Algorithms ◽  
Logarithmic Function ◽  
Planning And Scheduling ◽  
Linear Equality ◽  
Convex Inequality ◽  
Linear Equality Constraint ◽  
Mathematical Programming Problems

We consider the problem of minimizing a convex separable logarithmic function over a region defined by a convex inequality constraint or linear equality constraint, and two-sided bounds on the variables (box constraints). Such problems are interesting from both theoretical and practical point of view because they arise in some mathematical programming problems as well as in various practical problems such as problems of production planning and scheduling, allocation of resources, decision making, facility location problems, and so forth. Polynomial algorithms are proposed for solving problems of this form and their convergence is proved. Some examples and results of numerical experiments are also presented.

Neural Dynamics and Newton–Raphson Iteration for Nonlinear Optimization

2014 ◽  
Vol 9 (2) ◽  
Author(s):  
Dongsheng Guo ◽  
Yunong Zhang
Keyword(s):  
Nonlinear Optimization ◽  
Optimization Problems ◽  
Activation Function ◽  
Neural Dynamics ◽  
Time Varying ◽  
Step Size ◽  
Gradient Based ◽  
Digital Hardware ◽  
Newton Raphson ◽  
Raphson Iteration

In this paper, a special type of neural dynamics (ND) is generalized and investigated for time-varying and static scalar-valued nonlinear optimization. In addition, for comparative purpose, the gradient-based neural dynamics (or termed gradient dynamics (GD)) is studied for nonlinear optimization. Moreover, for possible digital hardware realization, discrete-time ND (DTND) models are developed. With the linear activation function used and with the step size being 1, the DTND model reduces to Newton–Raphson iteration (NRI) for solving the static nonlinear optimization problems. That is, the well-known NRI method can be viewed as a special case of the DTND model. Besides, the geometric representation of the ND models is given for time-varying nonlinear optimization. Numerical results demonstrate the efficacy and advantages of the proposed ND models for time-varying and static nonlinear optimization.

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