Stability of Generalised Equations and Variational Systems

该项目旨在推进一种新的变分分析数学理论，这可能导致在优化应用。当标准假设不满足时，重点将放在适合研究优化问题解的稳定性（“良好行为半径”）的正则性概念的扩展上，特别是那些具有平衡约束的半无限优化和程序。预期结果可能对提高数值方法的收敛性和促进解的后最优分析产生影响。它还可能产生新的工具，用于提高工程、物流、经济、金融系统和环境科学方面的效率和降低成本。

This project seeks to advance a new mathematical theory of variational analysis which may lead to applications in optimisation. The emphasis will be on extensions of regularity concepts appropriate for studying stability (the ‘radius of good behaviour’) of solutions to optimisation problems, particularly those of semi-infinite optimisation and programs with equilibrium constraints, when standard assumptions are not satisfied. The expected outcomes may have an impact in enhancing the convergence of numerical methods and facilitating the post-optimal analysis of solutions. It may also generate new tools for increasing efficiencies and cost reductions in engineering, logistics, economics, financial systems, and environmental science.