共轭梯度算法是求解大规模无约束优化问题最有效的方法之一。文章提出一种新型的修正PRP三项共轭梯度算法,该算法具有不依赖任何线搜索充分下降的特点,搜索方向具有信赖域特征。在较为温和条件下,算法全局收敛。数值实验表明,新算法是...共轭梯度算法是求解大规模无约束优化问题最有效的方法之一。文章提出一种新型的修正PRP三项共轭梯度算法,该算法具有不依赖任何线搜索充分下降的特点,搜索方向具有信赖域特征。在较为温和条件下,算法全局收敛。数值实验表明,新算法是有效的,比传统PRP三项共轭梯度算法更具竞争力。The conjugate gradient algorithm is one of the most effective methods for solving large-scale unconstrained optimization problems. This paper proposes a novel modified Polak-Ribière-Polyak (PRP) three-term conjugate gradient algorithm, which possesses the characteristic of ensuring sufficient descent without relying on any line search conditions. The search direction of this algorithm exhibits trust region properties. Under relatively mild conditions, the algorithm achieves global convergence. Numerical experiments demonstrate that the new algorithm is effective and more competitive compared to the classical PRP three-term conjugate gradient algorithm.展开更多
对于无约束优化问题,提出了一类新的三项记忆梯度算法.这类算法是在参数满足某些假设的条件下,确定它的取值范围,从而保证三项记忆梯度方向是使目标函数充分下降的方向.在非单调步长搜索下讨论了算法的全局收敛性.为了得到具有更好...对于无约束优化问题,提出了一类新的三项记忆梯度算法.这类算法是在参数满足某些假设的条件下,确定它的取值范围,从而保证三项记忆梯度方向是使目标函数充分下降的方向.在非单调步长搜索下讨论了算法的全局收敛性.为了得到具有更好收敛性质的算法,结合Solodov and Svaiter(2000)中的部分技巧,提出了一种新的记忆梯度投影算法,并证明了该算法在函数伪凸的情况下具有整体收敛性.展开更多
文摘共轭梯度算法是求解大规模无约束优化问题最有效的方法之一。文章提出一种新型的修正PRP三项共轭梯度算法,该算法具有不依赖任何线搜索充分下降的特点,搜索方向具有信赖域特征。在较为温和条件下,算法全局收敛。数值实验表明,新算法是有效的,比传统PRP三项共轭梯度算法更具竞争力。The conjugate gradient algorithm is one of the most effective methods for solving large-scale unconstrained optimization problems. This paper proposes a novel modified Polak-Ribière-Polyak (PRP) three-term conjugate gradient algorithm, which possesses the characteristic of ensuring sufficient descent without relying on any line search conditions. The search direction of this algorithm exhibits trust region properties. Under relatively mild conditions, the algorithm achieves global convergence. Numerical experiments demonstrate that the new algorithm is effective and more competitive compared to the classical PRP three-term conjugate gradient algorithm.
基金This work is supported by National Natural Science Foundation under Grant No.10571106.
文摘对于无约束优化问题,提出了一类新的三项记忆梯度算法.这类算法是在参数满足某些假设的条件下,确定它的取值范围,从而保证三项记忆梯度方向是使目标函数充分下降的方向.在非单调步长搜索下讨论了算法的全局收敛性.为了得到具有更好收敛性质的算法,结合Solodov and Svaiter(2000)中的部分技巧,提出了一种新的记忆梯度投影算法,并证明了该算法在函数伪凸的情况下具有整体收敛性.