一类非单调保守BFGS算法研究

基于非单调线搜索在寻求优化问题最优解中的优越性,提出了一类新的非单调保守BFGS算法.同已有方法不同,该算法中用来控制非单调性程度的算法参数不是取固定值,而是利用已有目标函数和梯度函数的信息自动调整其取值,以改善算法的数值表现.在合适的假设条件下,建立了新的非单调保守BFGS算法的全局收敛性.用基准测试优化问题测试了算...

INVESTIGATION ON A CLASS OF NONMONOTONE CAUTIOUS BFGS ALGORITHMS

With the superiority of nonmonotone line search in finding a solution of optimization problem, a class of nonmonotone cautious BFGS algorithms are developed. Different from the existing techniques of nonmonotone line search, the parameter, which is employed to control the magnitude of nonmonotonicity, is modified (not a fixed value) by the known information of the objective function and the gradient function such that the numerical performance of the developed algorithm is improved. Under some suitable assumptions, the global convergence is proved for this algorithm. Implementing the algorithm to solve some benchmark test problems, the results demonstrate that it is more effective than the similar algorithms.