一个新的对于无约束非凸优化问题渐近的算法

A new proximal algorithm for unconstrained nonconvex optimization problems

针对数学规划中的非凸函数的优化问题,根据已知的凸函数的优化结果及相应算法,构造新的渐进算法,并运用Kurdyka-Lojasiewicz不等式,对真下半连续的非凸函数的无约束非凸优化问题进行了收敛分析,得到了由改进的渐进算法生成的序列具有有限长且收敛于该函数的一个临界点.同时给出了序列收敛速率的结果表示.

For the optimization of nonconvex functions in mathematical programming,according to the known convex function optimization results and the corresponding algorithm,a new improved asymptotic algorithm is constructed,and by using Kurdyka-Lojasiewicz property,the convergence analysis of unconstrained nonconvex optimization problems for real lower semicontinuous nonconvex functions is considered.The sequence generated by the improved asymptotic algorithm has finite length and converges to a critical point of the function are obtained.Meanwhile,the result representation of the convergence rate of the sequence is given.