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

多极值全局连续优化中全局极小值的充要条件

• 批准号: DP0450151
• 负责人: Prof Vaithilingam Jeyakumar
• 金额: $ 19.67万
• 依托单位: The University of New South Wales
• 依托单位国家: 澳大利亚
• 项目类别: Discovery Projects
• 财政年份: 2004
• 资助国家: 澳大利亚
• 起止时间: 2004-01-31 至 2007-12-31
• 项目状态: 已结题
• 来源: https://dataportal.arc.gov.au/RGS/Web/Grants/DP0450151
• 关键词: Necessary; sufficient; conditions; global; minimum

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.

对寻找本地“最佳”（最佳）解决方案的机制的基本理解已是 通过优化技术实现。但是，解决全球优化问题，我们可能拥有许多本地最佳解决方案，这些解决方案不是“绝对最好的”（全球），对于许多在行业和科学中的应用至关重要，并且本质上是困难的。缺乏可验证的全球最佳条件是一个严重的限制。该项目将针对这些问题的许多类别开发此类全球最佳条件。 CIS开发的一种新方法，功能抽象的凸度，并显示出令人鼓舞的结果，将扩展并应用于解决这些问题。