一类带约束min-max-min问题的区间算法

An Interval Algorithm for a Class of Constrained min-max-min Problems

建立了一类带约束Min-Max-Min问题的数值方法,其中目标函数和约束条件均为Lipschitz连续函数。利用区间分析方法,基于罚函数法和区域二分原则,针对问题及目标函数约束条件的不可微的特点,构造了罚函数的区间扩张和无解区域删除原则,建立了区间算法,证明了该算法的收敛性。对算法进行了数值实验,并给出了数值算例,结果表明:该方法可以同时求出问题的最优值和全部全局最优解,是有效和可靠的。

An interval method for a class of constrained min-max-min problems is established, in which the objective functions and constrained functions are Lipsehitz continuous. Using the interval analysis and based on the penalty function and the region bisection method, and eontmposing the nondifferentiable trait of the problem and the constrained condition of the objective functions,the interval extensions of penalty functions and region deletion testing rules were constructed, the interval algorithm was established and convergence of algorithm was proven. Numerical experiments are performed to the algorithm and numerical results are presented. The results show that the method gets both the best value and all global solutions. The algorithm is effective and reliable.