Stability of Generalised Equations and Variational Systems

该项目旨在推进一个新的数学理论的变分分析，这可能会导致应用优化。重点将是适当的研究稳定性（“半径良好的行为”）的解决方案的优化问题，特别是那些半无限优化和平衡约束的程序，当标准的假设不满足的正则性概念的扩展。预期的结果可能会产生影响，在提高数值方法的收敛性，并促进解决方案的后优化分析。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的效率和成本降低。

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.