线性分式规划全局最优解的确定性方法

A Deterministic Global Optimization Method for Solving Linear Fractional Programming

针对分式规划问题的求解,给出一个确定性全局优化算法.首先将原问题转化为一个等价问题,然后利用线性化技巧,建立等价问题的松弛线性化问题.通过对可行域的不断剖分以及一系列松弛线性化问题的求解,逐步求得原问题的最优解.理论上证明了算法的收敛性,数值算例表明算法是可行的.

This paper presents a determined global optimization algorithm for solving linear fractional programming. After obtaining an equivalent problem of the initial problem through trasformation, then by using relaxation technique, the equivalent problem can be reduced to a sequence of linear programming problems. The proposed algorithm will be convergent to the global optimal solution by means of the subsequent solutions of the series of linear programming problems. Convergence of the algorithm is established and numerical results are given to show the feasibility and effectiveness.