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Tret'yakov Alexey Anatol'evich

Publications in Math-Net.Ru

  1. $P$-factor interpolation of solutions of an equation with a degenerate function

    Dokl. RAN. Math. Inf. Proc. Upr., 520:1 (2024),  5–10
  2. On the redundancy of Hessian nonsingularity for linear convergence rate of the Newton method applied to the minimization of convex functions

    Zh. Vychisl. Mat. Mat. Fiz., 64:4 (2024),  637–643
  3. Exact formula for solving a degenerate system of quadratic equations

    Zh. Vychisl. Mat. Mat. Fiz., 64:3 (2024),  387–391
  4. The method of fictitious extrema localization in the problem of global optimization

    Dokl. RAN. Math. Inf. Proc. Upr., 512 (2023),  78–80
  5. On the application of the solution of the degenerate nonlinear Burgers equation with a small parameter and the theory of $p$-regularity

    Dokl. RAN. Math. Inf. Proc. Upr., 512 (2023),  5–9
  6. $p$-Regularity theory and the existence of a solution to a boundary value problem continuously dependent on boundary conditions

    Zh. Vychisl. Mat. Mat. Fiz., 63:6 (2023),  920–936
  7. On the equivalence of singular and ill-posed problems: The $p$-factor regularization method

    Dokl. RAN. Math. Inf. Proc. Upr., 506 (2022),  41–44
  8. Convergence of continuous analogues of numerical methods for solving degenerate optimization problems and systems of nonlinear equations

    Zh. Vychisl. Mat. Mat. Fiz., 62:10 (2022),  1632–1638
  9. A new class of Lyapunov functions for stability analysis of singular dynamical systems. Elements of $p$-regularity theory

    Dokl. RAN. Math. Inf. Proc. Upr., 499 (2021),  8–12
  10. Some properties of smooth convex functions and Newton’s method

    Dokl. RAN. Math. Inf. Proc. Upr., 497 (2021),  12–17
  11. A new view of some fundamental results in optimization

    Zh. Vychisl. Mat. Mat. Fiz., 60:9 (2020),  1462–1471
  12. Locally polynomial method for solving systems of linear inequalities

    Zh. Vychisl. Mat. Mat. Fiz., 60:2 (2020),  216–220
  13. A new proof of the Kuhn–Tucker and Farkas theorems

    Zh. Vychisl. Mat. Mat. Fiz., 58:7 (2018),  1084–1088
  14. The $p$-order maximum principle for an irregular optimal control problem

    Zh. Vychisl. Mat. Mat. Fiz., 57:9 (2017),  1471–1476
  15. On reductibility of degenerate optimization problems to regular operator equations

    Zh. Vychisl. Mat. Mat. Fiz., 56:12 (2016),  2031
  16. $p$th-order approximation of the solution set of nonlinear equations

    Zh. Vychisl. Mat. Mat. Fiz., 53:12 (2013),  1951–1969
  17. New numerical methods and some applied aspects of the $p$-regularity theory

    Zh. Vychisl. Mat. Mat. Fiz., 46:11 (2006),  1987–2000
  18. The theorem on existence of singular solutions to nonlinear equations

    Tr. Petrozavodsk. Gos. Univ. Ser. Mat., 2005, no. 12,  22–36
  19. Solvability of the Cauchy Problem for a First-Order Partial Differential Equation in the Degenerate Case

    Differ. Uravn., 38:2 (2002),  216–221
  20. Convergence of the penalty function method for an unbounded solution set

    Zh. Vychisl. Mat. Mat. Fiz., 42:5 (2002),  641–652
  21. On the choice of a method for solving a general system of nonlinear equations

    Zh. Vychisl. Mat. Mat. Fiz., 41:5 (2001),  675–679
  22. A modified $2$-factor method for solving systems of nonlinear equations

    Zh. Vychisl. Mat. Mat. Fiz., 41:4 (2001),  558–569
  23. Generalization of the concept of $p$-regularity and higher order optimality conditions

    Zh. Vychisl. Mat. Mat. Fiz., 41:2 (2001),  207–216
  24. An approach to finding singular solutions to a general system of nonlinear equations

    Zh. Vychisl. Mat. Mat. Fiz., 40:3 (2000),  365–377
  25. Gradient method for linear approximate schemes

    Zh. Vychisl. Mat. Mat. Fiz., 39:10 (1999),  1625–1632
  26. On the stabilizing properties of the gradient method for unstable approximate schemes

    Zh. Vychisl. Mat. Mat. Fiz., 39:9 (1999),  1453–1463
  27. On the gradient method in a Hilbert space in the case of nonisolated minima

    Zh. Vychisl. Mat. Mat. Fiz., 39:4 (1999),  549–552
  28. Fast Wavelet Transform for Discrete Periodic Signals and Patterns

    Probl. Peredachi Inf., 34:2 (1998),  77–85
  29. Application of nonsmooth optimization methods to solving nonlinear operator equations

    Zh. Vychisl. Mat. Mat. Fiz., 38:9 (1998),  1452–1460
  30. Methods for finding singular solutions of nonlinear operator equations in the absence of 2-regularity

    Zh. Vychisl. Mat. Mat. Fiz., 37:10 (1997),  1157–1162
  31. On a local regularization of some classes of nonlinear operator equations

    Zh. Vychisl. Mat. Mat. Fiz., 36:7 (1996),  15–29
  32. The method of gradient descent for minimizing non-convex functions

    Zh. Vychisl. Mat. Mat. Fiz., 34:3 (1994),  344–359
  33. Factor analysis of nonlinear mappings and generalization of the notion of 2-regularity

    Zh. Vychisl. Mat. Mat. Fiz., 33:4 (1993),  631–634
  34. The reversibility of homogeneous polynomial mappings of degree $p$

    Zh. Vychisl. Mat. Mat. Fiz., 33:3 (1993),  323–334
  35. Properties of regular mathematical programming problems

    Zh. Vychisl. Mat. Mat. Fiz., 32:1 (1992),  162–167
  36. A model and a method for solving an extremal allocation problem in the design of high-speed computers

    Dokl. Akad. Nauk SSSR, 314:3 (1990),  573–575
  37. The interconnection between Lagrange's theorem and the geometry of feasible sets

    Dokl. Akad. Nauk SSSR, 300:6 (1988),  1289–1291
  38. Methods for solving degenerate problems

    Zh. Vychisl. Mat. Mat. Fiz., 28:7 (1988),  1097–1102
  39. The implicit function theorem in degenerate problems

    Uspekhi Mat. Nauk, 42:5(257) (1987),  215–216
  40. The unconditional minimization of non-convex functions

    Zh. Vychisl. Mat. Mat. Fiz., 27:11 (1987),  1752–1756
  41. On the choice of parameters in the method of penalty functions

    Zh. Vychisl. Mat. Mat. Fiz., 27:10 (1987),  1451–1461
  42. Stabilizing properties of the gradient method

    Zh. Vychisl. Mat. Mat. Fiz., 26:1 (1986),  134–137
  43. The accelerated Newton method for solving functional equations

    Dokl. Akad. Nauk SSSR, 281:6 (1985),  1293–1297
  44. Two schemes of the nonlinear optimization method in extremal problems

    Zh. Vychisl. Mat. Mat. Fiz., 24:7 (1984),  986–992
  45. Necessary and sufficient conditions for $P$th order optimality

    Zh. Vychisl. Mat. Mat. Fiz., 24:2 (1984),  203–209

© Steklov Math. Inst. of RAS, 2026