Local convergence analysis of augmented Lagrangian method for nonlinear semidefinite programming

Shiwei Wang () and Chao Ding ()
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Shiwei Wang: Chinese Academy of Sciences
Chao Ding: Chinese Academy of Sciences

Computational Optimization and Applications, 2024, vol. 87, issue 1, No 2, 39-81

Abstract: Abstract The augmented Lagrangian method (ALM) has gained tremendous popularity for its elegant theory and impressive numerical performance since it was proposed by Hestenes and Powell in 1969. It has been widely used in numerous efficient solvers to improve numerical performance to solve many problems. In this paper, without requiring the uniqueness of multipliers, the local (asymptotic Q-superlinear) Q-linear convergence rate of the primal-dual sequences generated by ALM for the nonlinear semidefinite programming is established by assuming the second-order sufficient condition and the semi-isolated calmness of the Karush–Kuhn–Tucker solution under some mild conditions.

Keywords: Nonlinear semidefinite programming; The augmented Lagrangian method; Local convergence rate; Semi-isolated calmness; Uniform quadratic growth; Uniform second order expansion; 90C22; 65K05; 49J52 (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s10589-023-00520-0

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