凸约束非线性方程组的杂交修正HS-FR共轭梯度解法

A Hybrid Modified HS-FR Conjugate Gradient Method for ConvexConstrained Nonlinear Equations

为改善求解凸约束非线性方程组的运算效率,基于共轭梯度算法和非线性方程组的基础研究,受凸组合技术和杂交思想的启发,采用修正HS(Hestenes-Stiefel)和FR(Fletcher-Reeves)共轭梯度参数的凸组合方法,构建了新的杂交共轭参数.证明了搜索方向具有充分下降性与信赖域性质.在适当的假设条件下,新算法的全局收敛性质.数值试验结果验证了新算法在求解大规模凸约束优化问题时的高效性与可行性.

In order to improve the operational efficiency for nonlinear equations with convex constraints,based on the studies of conjugate gradient methods and nonlinear equations and inspired by convex combination technique as well as the hybrid idea,a modified HS(Hestenes-Stiefel)and FR(Hestenes-Stiefel)conjugate gradient parameters is used to make a convex combination to construct a novel hybrid conjugate parameters.The search direction has sufficient descent and trust region properties.The global convergence of the new algorithm is proved under appropriate assumptions.The results of the numerical experiment verify the efficiency and feasibility of the new algorithm in solving large-scale convex constrained optimization problems.