最大熵原理在无约束优化方法中的应用

Application of Maximum Entropy Theory in Unconstrained Optimization

经研究，发现将最大滴原理与无约束优化方法相结合亦能达到约束优化公式化，简化优化的过程．使用罚函数法可将约束优化问题变成无约束优化问题，但原问题中的可微函数组成罚函数后有可能成为不可微问题，因而影响了再使用无约束优化方法中的诸多有效方法．如先使用最大熵原理找出原约束优化有关问题的等效Ｌａｇｒａｎｇｅ函数后，再构成罚函数即可保证是可微的了．

The application of maximum entropy theory in unconstrained optimization is disscussed in this paper. Combining maximum entropy theory with unconstrained constrained optimization formulation can be optimized and simplified. Constrained optimization problem can be expressed as unstrained optimuzation problem by using penality function, but differentiablity of the original problem may be lost, as a result many effective methods of unconstrained optimization may never be applicable. If maximum entropy is used to find lagrange function for the original constrained optimization, the penality function will be surely diffentiable.