Paper Info
Title
Z-type neural-dynamics for time-varying nonlinear optimization under a linear equality constraint with robot application.
Abstract
Nonlinear optimization is widely important for science and engineering. Most research in optimization has dealt with static nonlinear optimization while little has been done on time-varying nonlinear optimization problems. These are generally more complicated and demanding. We study time-varying nonlinear optimizations with time-varying linear equality constraints and adapt Z-type neural-dynamics (ZTND) for solving such problems. Using a Lagrange multipliers approach we construct a continuous ZTND model for such time-varying optimizations. A new four-instant finite difference (FIFD) formula is proposed that helps us discretize the continuous ZTND model with high accuracy. We propose the FDZTND-K and FDZTND-U discrete models and compare their quality and the advantage of the FIFD formula with two standard Euler-discretization ZTND models, called EDZTND-K and EDZTND-U that achieve lower accuracy. Theoretical convergence of our continuous and discrete models is proved and our methods are tested in numerical experiments. For a real world, we apply the FDZTND-U model to robot motion planning and show its feasibility in practice.
Year
DOI
Venue
2018
10.1016/j.cam.2017.06.017
Journal of Computational and Applied Mathematics
Keywords
Field
DocType
Z-type neural-dynamics,Time-varying nonlinear optimization,Linear equality constraint,Four-instant finite difference formula,Robot application
Convergence (routing),Continuous optimization,Discretization,Mathematical optimization,Nonlinear system,Mathematical analysis,Discrete optimization,Lagrange multiplier,Finite difference,Nonlinear programming,Mathematics
Journal
Volume
ISSN
Citations 
327
0377-0427
15
PageRank 
References 
Authors
0.56
18
4
Name
Order
Citations
PageRank
Jian Li1495.48
Mingzhi Mao2617.82
Frank Uhlig3191.48
Yunong Zhang42344162.43