线性约束优化的一类非单调信赖域算法

§1.引 言 考虑线性约束优化问题:min.f(x)s.t. aiTx=bi,i∈E,(1.1)aiTx≥bi,i∈I,其中f(x)是可行域X={x∈Rn|aiTx=bi,i∈E;aiTx≥bi,i∈I}上的连续可微函数. 多年来,问题(1.1)一直受到许多研究人员的广泛注意,相继提出了有效集方法、投影梯度法1,2]等.特别是近几年来,信赖域方法因具有强适性、强收敛性受到更多的重视3,8,11,12],这些方法都具有一个共同的性质:下降性,即要求在迭代点,目标函数值严格单调下降,放

A CLASS OF NONMONOTONE TRUST REGION ALGORITHMS FOR LINEARLY CONSTRAINED OPTIMIZATION

We present a class of nonmonotone trust region algorithms for linearly constrained optimization in this paper. The algorithm may adjust automatically the scope of the monotonicity by the degree that the quadratic model is "trusted". Under the suitable conditions, it is proved that any limit point of the infinite sequence generated by the algorithm is the Kuhn-Tucker point of the primal problem. Finally, some numerical results show that the new algorithm is very effective.