凹多乘子规划问题的全局优化算法

Global Optimization Algorithm for Concave Multiplicative Programming

针对广泛应用于经济管理、工程设计和证券分析等实际问题中的一类凹多乘子规划问题(P)给出了一全局优化算法。利用问题(P)的等价问题(P1)和函数的凹包络,建立了问题(P1)的松弛凸规划(PR1(H)),通过对(PR1(H))可行域的细分以及一系列(PR1(H))的求解过程,从理论上证明了算法收敛到问题(P)的全局最优解。

Abstract：In this paper a global optimization algorithm is proposed for concave muhiplicative programming problem （P） ,which can be applied to economic management,engineering design, and portfolio analysis,and so on. Utilizing the equivalent problem （ PI ） of problem （P） and concave envelope,relaxed convex programming （ PR1 （ H ） ） about problem （P1） is established, through the successive refinement of the convex relaxation of the feasible region of the objective function and the solutions of a series of （ PR1 （ H ） ）, and from theory the proof which the proposed algorithm is convergent to the global minimum is given.