Numerical method for a quadratic minimization problem with an ellipsoidal constraint and an a priori estimate for the solution norm

A. A. Dryazhenkov, M. M. Potapov

Faculty of Computational Mathematics and Cybernetics, Moscow State University, Moscow, 119991, Russia

Abstract: An algorithm for solving a quadratic minimization problem on an ellipsoidal set in a Hilbert space is proposed. The algorithm is stable to nonuniform perturbations of the operators. A key condition for its application is that we know an estimate for the norm of the exact solution. Applications to boundary control problems for the one-dimensional wave equation are considered. Numerical results are presented.

Key words: numerical method, quadratic minimization, ellipsoidal constraint, approximate data, stability, convergence.

UDC: 519.658

Received: 21.04.2015

DOI: 10.7868/S004446691602006X

 English version: Computational Mathematics and Mathematical Physics, 2016, 56:2, 206–220

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