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

对寻找局部“最佳”(最优)解决方案的机制有一个基本的理解 通过优化技术实现。然而，解决全局优化问题对于工业和科学中的许多应用来说是至关重要的，而且本质上是困难的。缺乏全局最优的可验证条件是一个严重的限制。该项目将为许多类别的此类问题开发可验证的全局最优性条件。一种新的方法，即函数抽象凸性，将被推广和应用于解决这些问题，该方法已经取得了良好的结果。

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.