Search Results - "Izmailov, A. F."

Newton-type methods near critical solutions of piecewise smooth nonlinear equations by Fischer, A, Izmailov, A. F, Jelitte, M

“…It is well-recognized that in the presence of singular (and in particular nonisolated) solutions of unconstrained or constrained smooth nonlinear equations,…”
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On attraction of linearly constrained Lagrangian methods and of stabilized and quasi-Newton SQP methods to critical multipliers by Izmailov, A. F., Solodov, M. V.

“…It has been previously demonstrated that in the case when a Lagrange multiplier associated to a given solution is not unique, Newton iterations [e.g., those of…”
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Critical Lagrange multipliers: what we currently know about them, how they spoil our lives, and what we can do about it by Izmailov, A. F., Solodov, M. V.

“…We discuss a certain special subset of Lagrange multipliers, called critical, which usually exist when multipliers associated to a given solution are not…”
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Accelerating convergence of a globalized sequential quadratic programming method to critical Lagrange multipliers by Izmailov, A. F.

“…This paper concerns the issue of asymptotic acceptance of the true Hessian and the full step by the sequential quadratic programming algorithm for…”
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Convergence rate estimates for penalty methods revisited by Izmailov, A. F., Solodov, M. V.

“…For the classical quadratic penalty, it is known that the distance from the solution of the penalty subproblem to the solution of the original problem is at…”
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Examples of dual behaviour of Newton-type methods on optimization problems with degenerate constraints by Izmailov, A. F., Solodov, M. V.

“…We discuss possible scenarios of behaviour of the dual part of sequences generated by primal-dual Newton-type methods when applied to optimization problems…”
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Unit stepsize for the Newton method close to critical solutions by Fischer, A., Izmailov, A. F., Solodov, M. V.

“…As is well known, when initialized close to a nonsingular solution of a smooth nonlinear equation, the Newton method converges to this solution superlinearly…”
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Stabilized SQP revisited by Izmailov, A. F., Solodov, M. V.

“…The stabilized version of the sequential quadratic programming algorithm (sSQP) had been developed in order to achieve superlinear convergence in situations…”
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Accelerating convergence of the globalized Newton method to critical solutions of nonlinear equations by Fischer, A., Izmailov, A. F., Solodov, M. V.

“…In the case of singular (and possibly even nonisolated) solutions of nonlinear equations, while superlinear convergence of the Newton method cannot be…”
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Critical solutions of nonlinear equations: stability issues by Izmailov, A. F., Kurennoy, A. S., Solodov, M. V.

“…It is known that when the set of Lagrange multipliers associated with a stationary point of a constrained optimization problem is not a singleton, this set may…”
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Critical solutions of nonlinear equations: local attraction for Newton-type methods by Izmailov, A. F., Kurennoy, A. S., Solodov, M. V.

“…We show that if the equation mapping is 2-regular at a solution in some nonzero direction in the null space of its Jacobian (in which case this solution is…”
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Constrained Lipschitzian Error Bounds and Noncritical Solutions of Constrained Equations by Fischer, A., Izmailov, A. F., Jelitte, M.

“…For many years, local Lipschitzian error bounds for systems of equations have been successfully used for the design and analysis of Newton-type methods. There…”
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A globally convergent Levenberg–Marquardt method for equality-constrained optimization by Izmailov, A. F., Solodov, M. V., Uskov, E. I.

“…It is well-known that the Levenberg–Marquardt method is a good choice for solving nonlinear equations, especially in the cases of singular/nonisolated…”
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Globalizing Stabilized Sequential Quadratic Programming Method by Smooth Primal-Dual Exact Penalty Function by Izmailov, A. F., Solodov, M. V., Uskov, E. I.

“…An iteration of the stabilized sequential quadratic programming method consists in solving a certain quadratic program in the primal-dual space, regularized in…”
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Stability of Possibly Nonisolated Solutions of Constrained Equations, with Applications to Complementarity and Equilibrium Problems by Arutyunov, A. V., Izmailov, A. F.

“…We present a new covering theorem for a nonlinear mapping on a convex cone, under the assumptions weaker than the classical Robinson’s regularity condition…”
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Subspace-stabilized sequential quadratic programming by Izmailov, A. F., Uskov, E. I.

“…The stabilized sequential quadratic programming (SQP) method has nice local convergence properties: it possesses local superlinear convergence under very mild…”
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Combining stabilized SQP with the augmented Lagrangian algorithm by Izmailov, A. F., Solodov, M. V., Uskov, E. I.

“…For an optimization problem with general equality and inequality constraints, we propose an algorithm which uses subproblems of the stabilized SQP (sSQP) type…”
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Attraction of Newton method to critical Lagrange multipliers: fully quadratic case by Izmailov, A. F., Uskov, E. I.

“…In this paper we continue the studies of the persistent effect of attraction of Newton-type iterations for optimality systems to critical Lagrange multipliers…”
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Newton-Type Methods: A Broader View by Izmailov, A. F., Solodov, M. V.

“…We discuss the question of which features and/or properties make a method for solving a given problem belong to the “Newtonian class.” Is it the strategy of…”
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New implementations of the 2-factor method by Izmailov, A. F.

“…The so-called 2-factor method was designed for finding singular solutions to nonlinear equations. New ways of implementing this method are proposed. So far,…”
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