单调全局最优化问题的凸化外逼近算法

单调优化是指目标函数与约束函数均为单调函数的全局优化问题．本文提出一种新的凸化变换方法把单调函数化为凸函数，进而把单调优化问题化为等价的凸极大或凹极小问题，然后采用Hoffman的外逼近方法来求得问题的全局最优解．我们把这种凸化方法同Tuy的Polyblock外逼近方法作了比较，通过数值比较可以看出本文提出的凸化的方法在收敛速度上明显优于Polyblock方法．

The Convexification Approximation Method for the Monetone Global Optimization

The monotone optimization is to maximize a monotone objective function constrained by monotone functions. This paper proposes a new convexification transformation method to convert a monotone function into a convex function. The monotone optimization problem can then be converted to an equivalent convex maximization or concave minimization problem. Thus we can adopt the Hoffman's outer approximation method to find the global optimal solution. We compare the proposed convexification method with Tuy's Ployblock outer approximation method. The illustrative example shows clearly that the convexification method is superior to the Tuy's method in solving the monotone problem.