Convergence of the Augmented Lagrangian Method for Nonlinear Optimization Problems over Second-Order Cones

Y. J. Liu () and L. W. Zhang ()
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Y. J. Liu: Shenyang Institute of Aeronautical Engineering
L. W. Zhang: Dalian University of Technology

Journal of Optimization Theory and Applications, 2008, vol. 139, issue 3, No 6, 557-575

Abstract: Abstract The paper analyzes the rate of local convergence of the augmented Lagrangian method for nonlinear second-order cone optimization problems. Under the constraint nondegeneracy condition and the strong second order sufficient condition, we demonstrate that the sequence of iterate points generated by the augmented Lagrangian method locally converges to a local minimizer at a linear rate, whose ratio constant is proportional to 1/τ with penalty parameter τ not less than a threshold $\hat{\tau}>0$ . Importantly and interestingly enough, the analysis does not require the strict complementarity condition.

Keywords: Augmented Lagrangian methods; Nonlinear second-order cone constrained optimization problems; Rates of local convergence; Semismooth functions (search for similar items in EconPapers)
Date: 2008
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Citations: View citations in EconPapers (6)

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DOI: 10.1007/s10957-008-9390-6

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