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中文摘要：
对一类带指数的凹多乘积规划问题，给出一种求其全局最优解的分支定界算法．先利用对数函数性质将原问题进行等价转化，对于等价问题，利用Lagrange弱对偶定理将分支定界算法中关键的定下界操作转化为易于求解的线性规划问题，且这些线性规划的规模不随迭代而变化，利于编程计算．同时，分支操作采用单纯形作为分割元素，并使用对分法，既保证穷举性，又使得线性规划的规模更小．最后给出算法的收敛性证明和数值实验结果．
英文摘要：
A global optimization method is presented for solving a class of concave mul- tiplicative programming problem with exponents. First, the problem is reformulated into an equivalent problem by using logarithmic property. The method is based on the branch and bound scheme and employs Lagrange duality theory to obtain the lower bounds. As a result, the lower-bounding subproblems during the algorithm search are all linear program- ming problems that can be solved very efficiently and that do not grow in size from iteration to iteration. So, the presented algorithm can be coded and applied to practical problems more easily. The simplex bisection is utilized for the partition of the presented algorithm. Then, the exhaustiveness is guaranteed and the scale of the relaxation linear programming problems can be smaller. Convergence of the method is proved and the numerical results are given to show the feasibility of the proposed method.
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