Optimization of subgradient method parameters on the base of rank-two correction of metric matrices

We establish a relaxation subgradient method (RSM) that includes parameter optimization utilizing metric rank-two correction matrices with a structure analogous to quasi-Newtonian (QN) methods. The metric matrix transformation consists of suppressing orthogonal and amplifying collinear components of the minimal length subgradient vector. The problem of constructing a metric matrix is formulated as a problem of solving an involved system of inequalities. Solving such system is based on a new learning algorithm. An estimate for its convergence rate is obtained depending on the parameters of the subgradient set. A new RSM has been developed and investigated on this basis. Computational experiments on complex large-scale functions confirm the effectiveness of the proposed algorithm. Tab. 4, bibliogr. 32.