机械灰色非线性优化的理论及其应用

探讨了含有灰参数的机械非线性优化理论与求解方法，通过引入灰数的概念，建立了机械优化设计中广义不确定性的灰凸集、灰凸规划的初步理论，提出了拓广的Kuhn-Tucker定理，得到了机械工程中一类含有灰色线性约束的灰色非线性优化模型的直接求解法，即将原非线性优化分解为等价的2个确定性边界模型直接求解。这不仅为机械优化设计提供了有效的手段，而且建立了确定性优化和非确定性优化的联系。最后通过含有灰系数线性约束与非线性目标函数的优化问题，说明机械灰色优化设计的直接求解方法研究的意义和实用性。

The Mechanical Grey Non-Linear Optimizing Theory and its Application

This Paper discussed mechanical non linear optimizing theory with Grey coefficient. By introducing the concept of Grey number, the general uncertainty primary theory with Grey convex set and Grey convex programming is established and developed wide Kuhn Tucker theorem is proposed. Then, a direct solution method to a sort of non linear programming with Grey linear restrictions is proposed in mechanical design and its characteristic is decomposing Grey non linear programming to two original non linear programming. It provides efficient measure for mechanical design and establishes the relation certainty optimizing and uncertainty optimizing.The Grey non linear optimizing possesses practicability and meaning to study.