一类非线性极小极大问题的粒子群-邻近点算法

Particle swarm optimization-proximal point algorithm for a class of nonlinear minimax problems

针对每个分量函数都是凸函数的离散型非线性极小极大问题,提出一种全局收敛的粒子群-邻近点混合算法。该算法利用极大熵函数将极小极大问题转化为一个光滑函数的无约束凸优化问题;利用邻近点算法为外层算法,内层算法采用粒子群算法来优化此问题;数值结果表明,该算法数值稳定性好、收敛快,是求解此类非线性极小极大问题的一种有效算法。

Aiming at the discrete nonlinear minimax problems with each component being convex function, this paper proposes a particle swarm optimization-proximal point algorithm with global convergence. This algorithm changes the minimax problem to the unconstrained optimization problem of smooth function by maximum entropy function. It uses the proximal point algorithm as the outer algorithm, and the particle swarm optimization as the internal algorithm. The numerical results show that this algorithm has the advantage of the fine stability, fast convergence speed and high precision, and it is an effective algorithm for nonlinear minimax problems.