Perturbation method and regularization of the Lagrange principle in nonlinear constrained optimization problems

DOI10.1134/S0965542524701677MaRDI QIDQ6661392

M. I. Sumin

Publication date: 13 January 2025

Published in: Computational Mathematics and Mathematical Physics (Search for Journal in Brave)

zbMATH Keywords

regularizationperturbation methodvalue functionFréchet subdifferentialregularizing algorithmproximal subgradientnonlinear constrained optimization problemmodified dual problemgeneralized minimizing sequenceoperator equality constraintLagrange multiplier rule in nondifferential form

Mathematics Subject Classification ID

Fréchet and Gateaux differentiability in optimization (49J50) Existence theories for free problems in two or more independent variables (49J10) Operations research, mathematical programming (90-XX)

Cites Work

• Stable sequential Kuhn-Tucker theorem in iterative form or a regularized Uzawa algorithm in a regular nonlinear programming problem
• Regularized parametric Kuhn-Tucker theorem in a Hilbert space
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• Variational Analysis and Generalized Differentiation I
• On the regularization of the Lagrange principle and on the construction of the generalized minimizing sequences in convex constrained optimization problems
• Nondifferential Kuhn–Tucker theorems in constrained extremum problems via subdifferentials of nonsmooth analysis
• On ill-posed problems, extremals of the Tikhonov functional and the regularized Lagrange principles
• Duality-based regularization in a linear convex mathematical programming problem
• Regularized dual method for nonlinear mathematical programming
• On regularization of the nondifferential Kuhn-Tucker theorem in a nonlinear problem for constrained extremum
• The perturbation method and regularization of the Lagrange multiplier rule in convex constrained optimization problems
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