Space-filling curves for numerical approximation and visualization of solutions to systems of nonlinear inequalities with applications in robotics
作者：
Highlights：
• Approximation of the solution set of systems of nonlinear inequalities is studied.
• Peano-Hilbert space-filling curves are applied for the dimensionality reduction.
• A Lipschitz global optimization method is proposed for approximating the solution set.
• Convergence conditions of the new method are established.
• Numerical experiments on finding workspace of robots confirm theoretical results.
摘要
•Approximation of the solution set of systems of nonlinear inequalities is studied.•Peano-Hilbert space-filling curves are applied for the dimensionality reduction.•A Lipschitz global optimization method is proposed for approximating the solution set.•Convergence conditions of the new method are established.•Numerical experiments on finding workspace of robots confirm theoretical results.
论文关键词：Systems of nonlinear inequalities,Space-filling curves,Global optimization,Derivative-free methods,Robot workspace
论文评审过程：Received 2 July 2020, Revised 24 August 2020, Accepted 30 August 2020, Available online 11 September 2020, Version of Record 11 September 2020.
论文官网地址：https://doi.org/10.1016/j.amc.2020.125660
