Far Eastern Mathematical Journal

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Minimization of an interval quadratic function in a Hilbert space


V. O. Filippova

2014, issue 2, Ñ. 270–279


Abstract
The problem of finding the minimum of a quadratic function with interval coefficients is considered. The concept of a $p$-universal solution to this problem is offered. The existence and uniqueness of $p$-universal solutions to the interval problem of minimization of a quadratic function is proved, an algorithm for finding them and their comparison are presented. As an application of the results the interval boundary value problem for the Poisson equation is examined.

Keywords:
interval problems, quadratic function, Lagrange principle

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References

[1] L. T. Ashhepkov, D. V. Davydov, Universal'nye resheniya interval'nyx zadach optimizacii i upravleniya, t. 151, Nauka, M, 2006.
[2] L. T. Aschepkov, D. V. Dolgy, “The universal solution of interval systems of linear algebraical equations”, Intern. J. Software Eng. and Knowledge Eng., 1993, 477–485.
[3] A. N. Tixonov, V. Ya. Arsenin, Metody resheniya nekorrektnyx zadach, Nauka, M, 1979.
[4] L. T. Ashhepkov, I. B. Kosogorova, “Minimizaciya kvadratichnoj funkcii s interval'nymi koe'fficientami”, Zhurnal vychislitel'noj matematiki i matematicheskoj fiziki, 42:5 (2002), 653–664.
[5] L. T. Ashhepkov, D. V. Davydov, “Stabilizaciya nablyudaemoj linejnoj sistemy upravleniya s postoyannymi interval'nymi koe'fficientami”, Matematika, Izv. VUZov, 477:2 (2002), 11–17.
[6] A. V. Zaxarov, Yu. I. Shokin, “Sintez sistem upravleniya priinterval'noj neopredelennosti parametrov i ix matematicheskix modelej”, Dokl. AN SSSR, 299:2 (1988).
[7] A. V. Lakeev, S. I. Noskov, “O mnozhestve reshenij linejnogo uravneniya s interval'no zadannym operatorom i pravoj chast'yu”, Sib. mat. zhurn., 35:5 (1994), 1074–1084.
[8] V. N. Shashixin, “Optimizaciya interval'nyx sistem”, Avtomatika i telemexanika, 11 (2000), 94–103.
[9] V. M. Alekseev, V. M. Tixomirov, S. V. Fomin, Optimal'noe upravlenie, FIZMATLIT, M., 2005, 384 s.

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