带扰动项的梯度法与混合投影法的收敛性分析

Convergence Analysis of Perturbed Gradient Methods and Hybrid Projection Methods

对无约束最优化问题提出了带扰动项的梯度法与混合投影法.我们在很一般的条件下,证明了由算法产生的迭代点列{x_k}满足:要么f(x_k)→-∞,要么f(x_k)收敛于有限值且▽f(x_k)→0.当f(x)是伪凸函数时,由带扰动项的混合投影算法产生的迭代点列{x_k}将收敛于问题的一个最优解以及其他一些精细的收敛性质.

For unconstrained optimization problem, we present perturbed gradient methods and hybrid projection methods. Under general conditions, we show that either f（xk）→-∞ or f（xk） converges to a finite value and △↓f（xk） →-∞ 0. If f（-） is quasi-convex, the perturbed projection methods force the sequence of iterates to a solution of the problem and some extended convergence results can be obtained.