针对离散极大极小函数综合是一类特殊的不可微最优化问题，提出了用可微最优化问题来逼近它的基本算法。为克服逼近问题的某些不良性质和状态，提出了非单调曲线搜索算法。应用上述算法构造了一种极大极小函数综合的求解方法，并在很弱的条件下得到了算法的收敛性。该方法具有算法简单，容易掌握和计算精度高等优点 Aiming at the synthesis of discrete minimax functions, which is a special kind of non-differentiable optimization problem, a basic algorithm is proposed to approximate it with the differentiable optimization problem. To overcome some bad properties and state of approximation problem, a non-monotone curve search algorithm is proposed. Using the above algorithm, a method of solving the maximal and minimal functions is constructed, and the convergence of the algorithm is obtained under very weak conditions. The method has the advantages of simple algorithm, easy to master and high computational accuracy