# On a regularized variant of the two-step projection-gradient method

F. P. Vasil'ev, T. V. Amochkina, Angelia Nedich

Research output: Contribution to journalArticle

### Abstract

A regularization method based on the two-step projection-gradient method along with the penalty function method is suggested for solving the minimization problem with incorrectly given assumed data. The sufficient conditions of convergence are presented. A minimization problem is considered with a given convex closed set from some Hilbert space H and some functions defined and Fresche differentiable over H. The problem is unstable to disturbances of the assumed data and it should be solved using the regularization methods.

Original language English (US) 35-42 8 Vestnik Moskovskogo Universiteta. Ser. 15 Vychislitel'naya Matematika i Kibernetika 1 Published - Jan 1996 Yes

### Fingerprint

Regularization Method
Minimization Problem
Penalty Function Method
Hilbert spaces
Closed set
Convex Sets
Differentiable
Disturbance
Hilbert space
Unstable
Sufficient Conditions

### ASJC Scopus subject areas

• Hardware and Architecture
• Software
• Applied Mathematics

### Cite this

On a regularized variant of the two-step projection-gradient method. / Vasil'ev, F. P.; Amochkina, T. V.; Nedich, Angelia.

In: Vestnik Moskovskogo Universiteta. Ser. 15 Vychislitel'naya Matematika i Kibernetika, No. 1, 01.1996, p. 35-42.

Research output: Contribution to journalArticle

title = "On a regularized variant of the two-step projection-gradient method",
abstract = "A regularization method based on the two-step projection-gradient method along with the penalty function method is suggested for solving the minimization problem with incorrectly given assumed data. The sufficient conditions of convergence are presented. A minimization problem is considered with a given convex closed set from some Hilbert space H and some functions defined and Fresche differentiable over H. The problem is unstable to disturbances of the assumed data and it should be solved using the regularization methods.",
author = "Vasil'ev, {F. P.} and Amochkina, {T. V.} and Angelia Nedich",
year = "1996",
month = "1",
language = "English (US)",
pages = "35--42",
journal = "Vestnik Moskovskogo Universiteta. Ser. 15 Vychislitel'naya Matematika i Kibernetika",
issn = "0137-0782",
publisher = "Izdatel'stvo Moskovskogo Gosudarstvennogo Universiteta im.M.V.Lomonosova/Publishing House of Moscow State University",
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AU - Vasil'ev, F. P.

AU - Amochkina, T. V.

AU - Nedich, Angelia

PY - 1996/1

Y1 - 1996/1

N2 - A regularization method based on the two-step projection-gradient method along with the penalty function method is suggested for solving the minimization problem with incorrectly given assumed data. The sufficient conditions of convergence are presented. A minimization problem is considered with a given convex closed set from some Hilbert space H and some functions defined and Fresche differentiable over H. The problem is unstable to disturbances of the assumed data and it should be solved using the regularization methods.

AB - A regularization method based on the two-step projection-gradient method along with the penalty function method is suggested for solving the minimization problem with incorrectly given assumed data. The sufficient conditions of convergence are presented. A minimization problem is considered with a given convex closed set from some Hilbert space H and some functions defined and Fresche differentiable over H. The problem is unstable to disturbances of the assumed data and it should be solved using the regularization methods.

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JO - Vestnik Moskovskogo Universiteta. Ser. 15 Vychislitel'naya Matematika i Kibernetika

JF - Vestnik Moskovskogo Universiteta. Ser. 15 Vychislitel'naya Matematika i Kibernetika

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ER -