@article {IOPORT.01671616,
    author       = {Kryazhimskii, A.V. and Paschenko, S.V.},
    title        = {On the problem of optimal compatibility.},
    year         = {2001},
    journal      = {Journal of Inverse and Ill-Posed Problems},
    volume       = {9},
    number       = {3},
    issn         = {0928-0219},
    pages        = {283-300},
    publisher    = {Walter de Gruyter, Berlin},
    abstract     = {The authors suggest a method of finding global solutions in the class $P$ of nonconvex optimization problems in a Hilbert space: minimizing $p$ such that $ p \ge p_0 $ and the system of linear equations $ G(p)x = b(p)$ is compatible in a convex set $X(p)$. The iterative algorithm for approaching the solution set of the minimization problem is based on the definition of the sequence $ (p_k, x_k), k \ge 0$ where $ x_{k+1} = x_k + \tau_{k+1} (u_{k+1} - x_k)$ and $ \tau_{k+1}, u_{k+1}$ are defined from two other separate optimal problems for the pair $(p_{k+1}, u_{k+1})$ and $\tau_{k+1}$. The accuracy estimates for approximate solutions are presented together with a constructive regularization algorithm for finding an approximate solution of an arbitrary problem from $P$ under a perturbed information on the associated functions $G(.)$ and $b(.)$.},
    reviewer     = {T.N.Pham (Hanoi)},
    identifier   = {01671616},
}