zbMATH — the first resource for mathematics

Continuous linearization method with a variable metric for problems in convex programming. (English. Russian original) Zbl 0947.90084
Comput. Math. Math. Phys. 37, No. 12, 1415-1421 (1997); translation from Zh. Vychisl. Mat. Mat. Fiz. 37, No. 12, 1459-1466 (1997).
A continuous method of linearization in a Hilbert space \(H\) with a variable metric is considered for solving minimization problems \[ J(u)\to\inf, \quad u\in{V}=\{u\in{H}\mid g_{i}(u)\leq{0},\;i=\overline{1,l}\} . \] The method proposed employs an operator \(G(u)\), which changes the metric of the space \(H\). In particular, when \(G(u)=J''(u)\) this method can be interpreted as the continuous counterpart of Newton’s method, which is a highly efficient computational tool for solving practical minimization problems. Its convergence is examined, a regularized variant of the method is proposed for problems with inaccurate input data.

90C25 Convex programming
65K05 Numerical mathematical programming methods