Necessary and sufficient conditions for global minimum in multi-extremal global continuous optimization

对寻找局部“最佳”（最优）解决方案的机制的基本理解是 通过优化技术实现。然而，解决全局优化问题，其中我们可能有许多局部最优解不是“绝对最佳”（全局），对于工业和科学中的许多应用至关重要，并且本质上是困难的。缺乏全局最优的可验证条件是一个严重的限制。这个项目将为这些问题的许多类别开发可验证的全局最优性条件。CI开发的一种新方法--函数抽象凸性方法已显示出良好的结果，将被扩展并应用于解决这些问题。

A basic understanding of the mechanisms for finding local "best" (optimal) solutions has been achieved through optimization techniques. However, solving global optimization problems, where we may have many local optimal solutions which are not the "absolutely best" (global), is vital for many applications in industry & science, and is intrinsically difficult. The lack of verifiable conditions for a global optimum is a serious limitation. This project will develop verifiable such global optimality conditions for many classes of these problems. A new methodology, functional abstract convexity, developed by CIs and has shown promising results, will be extended and applied for solving these problems.