一类线性多乘积规划的分支定界算法

A global Optimization Algorithm for a class of linear multiplicative programming

针对广泛应用于金融及经济等实际问题中的一类线性多乘积规划问题,提出一种分段线性化全局优化算法.首先将问题转化为等价问题,然后利用分段线性化技术得到问题目标函数和约束函数的线性下界,构造出等价问题的松弛线性规划,并从理论上证明了算法的收敛性.数值试验表明算法是有效可行的.

In this paper a piecewise linearization global Optimization Algorithm is proposed for the linear multiplicative programming,which has a lot of important applications in various areas such as financial optimization and economy plan.Firstly,the original program is transformed into the equivalent problems.Second,utilizing piecewise linearization technique,linear underestimates of the objective and constraint functions,linear relaxation programming for linear multiplicative programming is established over a rectangle,and the proposed global optimization algorithm is proposed that can converge to the globally optimal solution.And finally the numerical experiments are given to illustrate that the proposed algorithm is effective and feasible.