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Tret’yakov, Alexey A.

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Author ID: tretyakov.alexey-a Recent zbMATH articles by "Tret’yakov, Alexey A."
Published as: Tret’yakov, A. A.; Tret’yakov, Alexey A.; Tret’yakov, Alexey; Tretyakov, A. A.; Tretyakov, Alexey; Tretjakov, A. A.; Tret’yakov, A.; Tretyakov, Alexey A.
Documents Indexed: 134 Publications since 1974, including 2 Books
1 Contribution as Editor
Reviewing Activity: 624 Reviews
Co-Authors: 33 Co-Authors with 121 Joint Publications
552 Co-Co-Authors
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Serials

21 Doklady Mathematics
19 Computational Mathematics and Mathematical Physics
9 Zhurnal Vychislitel’noĭ Matematiki i Matematicheskoĭ Fiziki
6 U.S.S.R. Computational Mathematics and Mathematical Physics
4 Russian Journal of Numerical Analysis and Mathematical Modelling
3 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods
3 Vestnik St. Petersburg University. Mathematics
3 Boundary Value Problems
3 Optimization Letters
2 Numerical Functional Analysis and Optimization
2 SIAM Journal on Control and Optimization
2 Soviet Mathematics. Doklady
2 Moscow University Computational Mathematics and Cybernetics
2 Optimization
2 Journal of Computer and Systems Sciences International
2 Topological Methods in Nonlinear Analysis
2 Discussiones Mathematicae. Differential Inclusions, Control and Optimization
2 Communications on Pure and Applied Analysis
1 Problems of Information Transmission
1 Russian Mathematical Surveys
1 Ukrainian Mathematical Journal
1 Annales Universitatis Mariae Curie-Skłodowska. Sectio A. Mathematica
1 Calcolo
1 Control and Cybernetics
1 Journal of Optimization Theory and Applications
1 SIAM Journal on Numerical Analysis
1 Journal of Complexity
1 Computational Mathematics and Modeling
1 Soviet Physics. Doklady
1 Journal of Dynamics and Differential Equations
1 Set-Valued Analysis
1 Voprosy Kibernetiki (Moskva)
1 Vestnik Rossiĭskogo Universiteta Druzhby Narodov. Seriya Matematika
1 Kibernetika i Vychislitel’naya Tekhnika (Moskva)
1 Trudy Petrozavodskogo Gosudarstvennogo Universiteta. Seriya Matematika
1 Mathematical Communications
1 Mathematical Methods of Operations Research
1 Neliniĭni Kolyvannya
1 Issledovanie Operatsiĭ i ASU
1 Differential Equations
1 Carpathian Journal of Mathematics
1 Vychislitel’nye Metody i Programmirovanie
1 Journal of Mathematics and Applications
1 Set-Valued and Variational Analysis
1 TWMS Journal of Pure and Applied Mathematics

Publications by Year

Citations contained in zbMATH Open

61 Publications have been cited 233 times in 81 Documents Cited by Year
Factor-analysis of nonlinear mappings: \(p\)-regularity theory. Zbl 1053.58004
Tret’yakov, Alexey; Marsden, Jerrold E.
25
2003
Optimality conditions for degenerate extremum problems with equality constraints. Zbl 1037.49025
Brezhneva, Olga A.; Tret’yakov, Alexey A.
21
2003
Necessary and sufficient conditions for optimality of P-th order. Zbl 0562.49013
Tret’yakov, A. A.
20
1984
The implicit function theorem in degenerate problems. Zbl 0683.58008
Tret’yakov, A. A.
16
1987
Methods for solving degenerate problems. Zbl 0684.65051
Belash, K. N.; Tret’yakov, A. A.
11
1988
2-regular solutions of nonlinear problems. Theory and numerical methods. (2-регулярные решения нелинейных задач: теория и численные методы.) Zbl 0965.47050
Izmailov, A. F.; Tret’yakov, A. A.
11
1999
The \(p\)th-order optimality conditions for inequality constrained optimization problems. Zbl 1224.90206
Brezhneva, O. A.; Tret’yakov, A. A.
8
2005
The method of gradient descent for minimizing non-convex functions. Zbl 0817.49028
Izmailov, A. F.; Tret’yakov, A. A.
7
1994
An elementary proof of the Karush-Kuhn-Tucker theorem in normed linear spaces for problems with a finite number of inequality constraints. Zbl 1222.90080
Brezhneva, Olga; Tret’yakov, Alexey A.
6
2011
On the existence of solutions to nonlinear equations involving singular mappings with non-zero \(p\)-kernel. Zbl 1235.47054
Prusińska, Agnieszka; Tret’yakov, Alexey A.
6
2011
The \(p\)th order optimality conditions for nonregular optimization problems. Zbl 1211.90244
Brezhneva, O. A.; Tret’yakov, A. A.
5
2008
\(p\)-factor methods for nonregular inequality-constrained optimization problems. Zbl 1165.90648
Szczepanik, Ewa; Tret’yakov, Alexey
5
2008
The \(p\)-factor-Lagrange methods for degenerate nonlinear programming. Zbl 1133.90396
Brezhneva, Olga A.; Tret’yakov, Alexey A.
5
2007
A remark on the existence of solutions to nonlinear equations with degenerate mappings. Zbl 1154.47050
Prusińska, Agnieszka; Tret’yakov, Alexey
5
2008
Implicit function theorems for nonregular mappings in Banach spaces. Exit from singularity. Zbl 1143.47042
Brezhneva, Olga A.; Tret’yakov, Alexey A.
4
2007
Higher-order implicit function theorems and degenerate nonlinear boundary-value problems. Zbl 1156.34013
Brezhneva, Olga A.; Tret’yakov, Alexey A.; Marsden, Jerrold E.
4
2008
A simple and elementary proof of the Karush-Kuhn-Tucker theorem for inequality-constrained optimization. Zbl 1154.90587
Brezhneva, Olga A.; Tret’yakov, Alexey A.; Wright, Stephen E.
4
2009
\(p\)-regularity theory. Tangent cone description in the singular case. Zbl 1458.46067
Prusińska, A.; Tret’yakov, A.
4
2016
High order stability conditions for degenerate optimization problems; elements of \(p\)-regularity theory. Zbl 1229.90211
Bednarczuk, Ewa; Prusińska, Agnieszka; Tret’yakov, Alexey A.
4
2011
The 2-factor-method with a modified Lagrange function for degenerate constrained optimization problems. Zbl 1327.90302
Brezhneva, O. A.; Evtushenko, Yu. G.; Tret’yakov, A. A.
3
2006
Necessary and sufficient optimality conditions of p-th order. Zbl 0537.49009
Tret’yakov, A. A.
3
1984
New methods for solving essentially nonlinear problems. (Novye metody resheniya sushchestvenno nelinejnykh problem.) Zbl 0993.65062
Brezhneva, O. A.; Tret’yakov, A. A.
3
2000
On the choice of a method for solving a general system of nonlinear equations. Zbl 1018.47046
Brezhneva, O. A.; Tret’yakov, A. A.
3
2001
\(p\)th-order approximation of the solution set of nonlinear equations. Zbl 1313.47147
Evtushenko, Yu. G.; Tret’yakov, A. A.
3
2013
Two schemes for a non-linear method of optimization in extremal problems. Zbl 0588.90080
Tret’yakov, A. A.
2
1984
The stabilizing properties of the gradient method. Zbl 0641.90063
Bereznëv, V. A.; Karmanov, V. G.; Tret’yakov, A. A.
2
1986
Methods for solving degenerate problems. Zbl 0653.65039
Balash, K. N.; Tret’yakov, A. A.
2
1988
Application of \(p\)-regularity theory to nonlinear boundary value problems. Zbl 1306.47074
Grzegorczyk, Wiesław; Medak, Beata; Tret’yakov, Alexey A.
2
2013
\(p\)th-order numerical methods for solving systems of nonlinear equations. Zbl 1301.65038
Evtushenko, Yu. G.; Tret’yakov, A. A.
2
2014
Existence of periodic solutions to nonlinear \(p\)-regular boundary value problem. Zbl 1344.37020
Medak, Beata; Tret’yakov, Alexey A.
2
2015
Elementary proof of classical necessary optimality conditions for a mathematical programming problem with inequality constraints. Zbl 1180.49020
Tret’yakov, A. A.
2
2009
Solvability of the Cauchy problem for a first-order partial differential equation in the degenerate case. Zbl 1029.35065
Brezhneva, O. A.; Tret’yakov, A. A.
2
2002
Elementary proof of constructive versions of the tangent direction theorem and the implicit function theorem. Zbl 1251.26011
Evtushenko, Yu. G.; Tret’yakov, A. A.
2
2012
\(p\)-regular nonlinearity: tangency at singularity in degenerate optimization problems. Zbl 1458.46063
Bednarczuk, Ewa M.; Tretyakov, Alexey
2
2017
New approach to optimality conditions for degenerate nonlinear programming problems. Zbl 1342.90179
Brezhneva, O. A.; Tret’yakov, A. A.
1
2016
Generalization of \(p\)-regularity notion and tangent cone description in the singular case. Zbl 1317.58012
Grzegorczyk, Wiesław; Medak, Beata; Tret’yakov, Alexey A.
1
2012
Exact differentiable penalty for a problem of quadratic programming with the use of a gradient-projective method. Zbl 1309.90074
Tret’yakov, Alexey; Tyrtyshnikov, Eugene
1
2015
\(p\)-order necessary and sufficient conditions for optimality in singular calculus of variations. Zbl 1237.49027
Prusińska, Agnieszka; Tret’yakov, Alexey
1
2010
P-factor-approach to degenerate optimization problems. Zbl 1219.90160
Brezhneva, O. A.; Tret’yakov, A. A.
1
2006
On stabilizing properties of the gradient method. Zbl 0613.90079
Bereznëv, V. A.; Karmanov, V. G.; Tret’yakov, A. A.
1
1986
The accelerated Newton method for the solution of functional equations. Zbl 0618.65048
Denisov, D. V.; Karmanov, V. G.; Tret’yakov, A. A.
1
1985
An approach to finding singular solutions to a general system of nonlinear equations. Zbl 0990.65056
Brezhneva, O. A.; Izmailov, A. F.; Tret’yakov, A. A.; Khmura, A.
1
2000
A modified 2-factor method for solving systems of nonlinear equations. Zbl 1022.65056
Brezhneva, O. A.; Tret’yakov, A. A.; Chmura, A.
1
2001
Necessary \(p\)-th order optimality conditions for irregular Lagrange problem in calculus of variations. Zbl 1308.90197
Prusińska, Agnieszka; Tret’yakov, Alexey
1
2014
\(p\)-regular nonlinear dynamics. Zbl 1309.34071
Medak, B.; Tret’yakov, A. A.
1
2014
Iterative method for solving nonlinear singular problems. Zbl 1377.65058
Prusińska, Agnieszka; Tret’yakov, Alexey
1
2016
When the Karush-Kuhn-Tucker theorem fails: constraint qualifications and higher-order optimality conditions for degenerate optimization problems. Zbl 1377.49025
Brezhneva, Olga; Tret’yakov, Alexey A.
1
2017
Regularization of linear approximate schemes by the gradient descent. Zbl 1004.65066
Izmailov, Alexey F.; Karmanov, Vladimir G.; Tretyakov, Alexey A.
1
2001
On the gradient method in a Hilbert space in the case of nonisolated minima. Zbl 0964.90058
Izmailov, A. F.; Tret’yakov, A. A.
1
1999
A finite-termination gradient projection method for solving systems of linear inequalities. Zbl 1193.65102
Tret’yakov, A. A.
1
2010
Solutions to some singular nonlinear boundary value problems. Zbl 1293.35324
Medak, Beata; Tret’yakov, Alexey A.; Żołądek, Henryk
1
2013
A finite gradient-projective solver for a quadratic programming problem. Zbl 1296.65092
Tret’yakov, A.; Tyrtyshnikov, E. E.
1
2013
A short elementary proof of the Lagrange multiplier theorem. Zbl 1259.90129
Brezhneva, Olga; Tret’yakov, Alexey A.; Wright, Stephen E.
1
2012
Corrigendum: optimality conditions for degenerate extremum problems with equality constraints. Zbl 1201.49025
Brezhneva, Olga; Tret’yakov, Alexey A.
1
2010
The \(p\)-regularity theory and Poincaré’s small parameter method. Zbl 1208.34089
Brezhneva, O. A.; Evtushenko, Yu. G.; Tret’yakov, A. A.
1
2006
On solution existence for the perturbed degenerate optimization problem with equality constraints: \(p\)-order stability condition. Zbl 1205.49010
Tret’yakov, A. A.
1
2010
\(p\)th order Kuhn-Tucker-type optimality conditions for a singular inequality constrained optimization problem. Zbl 1211.90240
Tret’yakov, A. A.
1
2010
Application of \(p\)-regularity theory to the Duffing equation. Zbl 1484.34093
Medak, Beata; Tret’yakov, Alexey A.
1
2017
Partitioning, orthogonality, and permutations. Zbl 1043.94003
Malozemov, V. N.; Tret’yakov, A. A.
1
1999
On a local regularization of some classes of nonlinear operator equations. Zbl 1161.65331
Izmailov, A. F.; Tret’yakov, A. A.
1
1996
New approach to Farkas’ theorem of the alternative. Zbl 1428.46002
Evtushenko, Yu. G.; Tret’yakov, A. A.; Tyrtyshnikov, E. E.
1
2019
New approach to Farkas’ theorem of the alternative. Zbl 1428.46002
Evtushenko, Yu. G.; Tret’yakov, A. A.; Tyrtyshnikov, E. E.
1
2019
\(p\)-regular nonlinearity: tangency at singularity in degenerate optimization problems. Zbl 1458.46063
Bednarczuk, Ewa M.; Tretyakov, Alexey
2
2017
When the Karush-Kuhn-Tucker theorem fails: constraint qualifications and higher-order optimality conditions for degenerate optimization problems. Zbl 1377.49025
Brezhneva, Olga; Tret’yakov, Alexey A.
1
2017
Application of \(p\)-regularity theory to the Duffing equation. Zbl 1484.34093
Medak, Beata; Tret’yakov, Alexey A.
1
2017
\(p\)-regularity theory. Tangent cone description in the singular case. Zbl 1458.46067
Prusińska, A.; Tret’yakov, A.
4
2016
New approach to optimality conditions for degenerate nonlinear programming problems. Zbl 1342.90179
Brezhneva, O. A.; Tret’yakov, A. A.
1
2016
Iterative method for solving nonlinear singular problems. Zbl 1377.65058
Prusińska, Agnieszka; Tret’yakov, Alexey
1
2016
Existence of periodic solutions to nonlinear \(p\)-regular boundary value problem. Zbl 1344.37020
Medak, Beata; Tret’yakov, Alexey A.
2
2015
Exact differentiable penalty for a problem of quadratic programming with the use of a gradient-projective method. Zbl 1309.90074
Tret’yakov, Alexey; Tyrtyshnikov, Eugene
1
2015
\(p\)th-order numerical methods for solving systems of nonlinear equations. Zbl 1301.65038
Evtushenko, Yu. G.; Tret’yakov, A. A.
2
2014
Necessary \(p\)-th order optimality conditions for irregular Lagrange problem in calculus of variations. Zbl 1308.90197
Prusińska, Agnieszka; Tret’yakov, Alexey
1
2014
\(p\)-regular nonlinear dynamics. Zbl 1309.34071
Medak, B.; Tret’yakov, A. A.
1
2014
\(p\)th-order approximation of the solution set of nonlinear equations. Zbl 1313.47147
Evtushenko, Yu. G.; Tret’yakov, A. A.
3
2013
Application of \(p\)-regularity theory to nonlinear boundary value problems. Zbl 1306.47074
Grzegorczyk, Wiesław; Medak, Beata; Tret’yakov, Alexey A.
2
2013
Solutions to some singular nonlinear boundary value problems. Zbl 1293.35324
Medak, Beata; Tret’yakov, Alexey A.; Żołądek, Henryk
1
2013
A finite gradient-projective solver for a quadratic programming problem. Zbl 1296.65092
Tret’yakov, A.; Tyrtyshnikov, E. E.
1
2013
Elementary proof of constructive versions of the tangent direction theorem and the implicit function theorem. Zbl 1251.26011
Evtushenko, Yu. G.; Tret’yakov, A. A.
2
2012
Generalization of \(p\)-regularity notion and tangent cone description in the singular case. Zbl 1317.58012
Grzegorczyk, Wiesław; Medak, Beata; Tret’yakov, Alexey A.
1
2012
A short elementary proof of the Lagrange multiplier theorem. Zbl 1259.90129
Brezhneva, Olga; Tret’yakov, Alexey A.; Wright, Stephen E.
1
2012
An elementary proof of the Karush-Kuhn-Tucker theorem in normed linear spaces for problems with a finite number of inequality constraints. Zbl 1222.90080
Brezhneva, Olga; Tret’yakov, Alexey A.
6
2011
On the existence of solutions to nonlinear equations involving singular mappings with non-zero \(p\)-kernel. Zbl 1235.47054
Prusińska, Agnieszka; Tret’yakov, Alexey A.
6
2011
High order stability conditions for degenerate optimization problems; elements of \(p\)-regularity theory. Zbl 1229.90211
Bednarczuk, Ewa; Prusińska, Agnieszka; Tret’yakov, Alexey A.
4
2011
\(p\)-order necessary and sufficient conditions for optimality in singular calculus of variations. Zbl 1237.49027
Prusińska, Agnieszka; Tret’yakov, Alexey
1
2010
A finite-termination gradient projection method for solving systems of linear inequalities. Zbl 1193.65102
Tret’yakov, A. A.
1
2010
Corrigendum: optimality conditions for degenerate extremum problems with equality constraints. Zbl 1201.49025
Brezhneva, Olga; Tret’yakov, Alexey A.
1
2010
On solution existence for the perturbed degenerate optimization problem with equality constraints: \(p\)-order stability condition. Zbl 1205.49010
Tret’yakov, A. A.
1
2010
\(p\)th order Kuhn-Tucker-type optimality conditions for a singular inequality constrained optimization problem. Zbl 1211.90240
Tret’yakov, A. A.
1
2010
A simple and elementary proof of the Karush-Kuhn-Tucker theorem for inequality-constrained optimization. Zbl 1154.90587
Brezhneva, Olga A.; Tret’yakov, Alexey A.; Wright, Stephen E.
4
2009
Elementary proof of classical necessary optimality conditions for a mathematical programming problem with inequality constraints. Zbl 1180.49020
Tret’yakov, A. A.
2
2009
The \(p\)th order optimality conditions for nonregular optimization problems. Zbl 1211.90244
Brezhneva, O. A.; Tret’yakov, A. A.
5
2008
\(p\)-factor methods for nonregular inequality-constrained optimization problems. Zbl 1165.90648
Szczepanik, Ewa; Tret’yakov, Alexey
5
2008
A remark on the existence of solutions to nonlinear equations with degenerate mappings. Zbl 1154.47050
Prusińska, Agnieszka; Tret’yakov, Alexey
5
2008
Higher-order implicit function theorems and degenerate nonlinear boundary-value problems. Zbl 1156.34013
Brezhneva, Olga A.; Tret’yakov, Alexey A.; Marsden, Jerrold E.
4
2008
The \(p\)-factor-Lagrange methods for degenerate nonlinear programming. Zbl 1133.90396
Brezhneva, Olga A.; Tret’yakov, Alexey A.
5
2007
Implicit function theorems for nonregular mappings in Banach spaces. Exit from singularity. Zbl 1143.47042
Brezhneva, Olga A.; Tret’yakov, Alexey A.
4
2007
The 2-factor-method with a modified Lagrange function for degenerate constrained optimization problems. Zbl 1327.90302
Brezhneva, O. A.; Evtushenko, Yu. G.; Tret’yakov, A. A.
3
2006
P-factor-approach to degenerate optimization problems. Zbl 1219.90160
Brezhneva, O. A.; Tret’yakov, A. A.
1
2006
The \(p\)-regularity theory and Poincaré’s small parameter method. Zbl 1208.34089
Brezhneva, O. A.; Evtushenko, Yu. G.; Tret’yakov, A. A.
1
2006
The \(p\)th-order optimality conditions for inequality constrained optimization problems. Zbl 1224.90206
Brezhneva, O. A.; Tret’yakov, A. A.
8
2005
Factor-analysis of nonlinear mappings: \(p\)-regularity theory. Zbl 1053.58004
Tret’yakov, Alexey; Marsden, Jerrold E.
25
2003
Optimality conditions for degenerate extremum problems with equality constraints. Zbl 1037.49025
Brezhneva, Olga A.; Tret’yakov, Alexey A.
21
2003
Solvability of the Cauchy problem for a first-order partial differential equation in the degenerate case. Zbl 1029.35065
Brezhneva, O. A.; Tret’yakov, A. A.
2
2002
On the choice of a method for solving a general system of nonlinear equations. Zbl 1018.47046
Brezhneva, O. A.; Tret’yakov, A. A.
3
2001
A modified 2-factor method for solving systems of nonlinear equations. Zbl 1022.65056
Brezhneva, O. A.; Tret’yakov, A. A.; Chmura, A.
1
2001
Regularization of linear approximate schemes by the gradient descent. Zbl 1004.65066
Izmailov, Alexey F.; Karmanov, Vladimir G.; Tretyakov, Alexey A.
1
2001
New methods for solving essentially nonlinear problems. (Novye metody resheniya sushchestvenno nelinejnykh problem.) Zbl 0993.65062
Brezhneva, O. A.; Tret’yakov, A. A.
3
2000
An approach to finding singular solutions to a general system of nonlinear equations. Zbl 0990.65056
Brezhneva, O. A.; Izmailov, A. F.; Tret’yakov, A. A.; Khmura, A.
1
2000
2-regular solutions of nonlinear problems. Theory and numerical methods. (2-регулярные решения нелинейных задач: теория и численные методы.) Zbl 0965.47050
Izmailov, A. F.; Tret’yakov, A. A.
11
1999
On the gradient method in a Hilbert space in the case of nonisolated minima. Zbl 0964.90058
Izmailov, A. F.; Tret’yakov, A. A.
1
1999
Partitioning, orthogonality, and permutations. Zbl 1043.94003
Malozemov, V. N.; Tret’yakov, A. A.
1
1999
On a local regularization of some classes of nonlinear operator equations. Zbl 1161.65331
Izmailov, A. F.; Tret’yakov, A. A.
1
1996
The method of gradient descent for minimizing non-convex functions. Zbl 0817.49028
Izmailov, A. F.; Tret’yakov, A. A.
7
1994
Methods for solving degenerate problems. Zbl 0684.65051
Belash, K. N.; Tret’yakov, A. A.
11
1988
Methods for solving degenerate problems. Zbl 0653.65039
Balash, K. N.; Tret’yakov, A. A.
2
1988
The implicit function theorem in degenerate problems. Zbl 0683.58008
Tret’yakov, A. A.
16
1987
The stabilizing properties of the gradient method. Zbl 0641.90063
Bereznëv, V. A.; Karmanov, V. G.; Tret’yakov, A. A.
2
1986
On stabilizing properties of the gradient method. Zbl 0613.90079
Bereznëv, V. A.; Karmanov, V. G.; Tret’yakov, A. A.
1
1986
The accelerated Newton method for the solution of functional equations. Zbl 0618.65048
Denisov, D. V.; Karmanov, V. G.; Tret’yakov, A. A.
1
1985
Necessary and sufficient conditions for optimality of P-th order. Zbl 0562.49013
Tret’yakov, A. A.
20
1984
Necessary and sufficient optimality conditions of p-th order. Zbl 0537.49009
Tret’yakov, A. A.
3
1984
Two schemes for a non-linear method of optimization in extremal problems. Zbl 0588.90080
Tret’yakov, A. A.
2
1984

Citations by Year