Zhao Yingfeng, Yang Juanjuan
School of Mathematical Science, Henan Institute of Science and Technology, Xinxiang, China.
J Inequal Appl. 2018;2018(1):354. doi: 10.1186/s13660-018-1947-9. Epub 2018 Dec 20.
An efficient inner approximation algorithm is presented for solving the generalized linear multiplicative programming problem with generalized linear multiplicative constraints. The problem is firstly converted into an equivalent generalized geometric programming problem, then some magnifying-shrinking skills and approximation strategies are used to convert the equivalent generalized geometric programming problem into a series of posynomial geometric programming problems that can be solved globally. Finally, we prove the convergence property and some practical application examples in optimal design domain, and arithmetic examples taken from recent literatures and GLOBALLib are carried out to validate the performance of the proposed algorithm.
针对具有广义线性乘法约束的广义线性乘法规划问题，提出了一种有效的内逼近算法。该问题首先被转化为一个等价的广义几何规划问题，然后运用一些放大缩小技巧和逼近策略，将等价的广义几何规划问题转化为一系列可全局求解的正项式几何规划问题。最后，我们证明了收敛性，并给出了在优化设计领域的一些实际应用例子，还进行了取自近期文献和GLOBALLib的算例来验证所提算法的性能。
