论文标题
log-sum-exp优化问题受Lukasiewicz的模糊关系不平等
Log-sum-exp optimization problem subjected to Lukasiewicz fuzzy relational inequalities
论文作者
论文摘要
在本文中，我们引入了一个非线性优化问题，其目标函数是凸面log-sum-exp函数，可行区域被定义为Lukasiewicz t-norm定义的模糊关系不平等（FRI）系统。得出了一些必要和足够的条件，以确定问题的可行性。可行的溶液集以有限数量的封闭凸单元而表征。由于可行的Fris解决方案是非凸的，因此可能不会直接采用常规方法。提出了一种用于解决此非线性问题的算法。事实证明，算法可以找到确切的最佳解决方案，并提出一个示例以说明所提出的算法。
In this paper, we introduce a nonlinear optimization problem whose objective function is the convex log-sum-exp function and the feasible region is defined as a system of fuzzy relational inequalities (FRI) defined by the Lukasiewicz t-norm. Some necessary and sufficient conditions are derived to determine the feasibility of the problem. The feasible solution set is characterized in terms of a finite number of closed convex cells. Since the feasible solutions set of FRIs is non-convex, conventional methods may not be directly employed. An algorithm is presented for solving this nonlinear problem. It is proved that the algorithm can find the exact optimal solution and an example is presented to illustrate the proposed algorithm.
