【摘要】 本文讨论了两个与柯西不等式有关的整数规划问题:其一是求和为常数的 n 个正整数的乘积之最大值,其二是求积为常数的 n 个正整数之和的最小值。对第一个问题,找到了求解公式,对第二个问题,得到了特殊情况下求解公式和一般情况下最优解的必要条件,并进而得到了求解第二问题的一种局部搜索方法,并得出两个问题的可行解数目的计数公式。更多还原

【Abstract】 In this paper we discuss two integer programming problems relating to Cauchy inequality.The first is to determine the maximum value of product of n positive integers whose sum is a constant.The second is to determine the minimum value of sum of n positive integers whose product is a constant.For solving the first one a formula is presented.For the second,a formula is presented for getting the optimal solution in a special case.As for general case,the necessary condition for optimality is presented,on which alocal search method is designed for the second problem.In addition,two formulas for counting number of feasible solutions of the two problems are presented.更多还原