An Implementable Augmented Lagrangian Method for Solving Second-Order Cone Constrained Variational Inequalities

Yining Sun (), Li Wang, Juhe Sun (), Bin Wang () and Yanhong Yuan ()
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Yining Sun: School of Science, Shenyang Aerospace University, Shenyang 110136, P. R. China
Li Wang: School of Science, Shenyang Aerospace University, Shenyang 110136, P. R. China
Juhe Sun: School of Science, Shenyang Aerospace University, Shenyang 110136, P. R. China
Bin Wang: School of Science, Shenyang Aerospace University, Shenyang 110136, P. R. China
Yanhong Yuan: College of Economics and Management, Taiyuan University of Technology, Taiyuan, 030024, P. R. China

Asia-Pacific Journal of Operational Research (APJOR), 2023, vol. 40, issue 03, 1-19

Abstract: In this paper, we construct an implementable augmented Lagrangian method to solve second-order cone constrained variational inequalities (SOCCVI) problem. By considering a special optimization problem that has the same solution as the SOCCVI problem, we obtain different equivalent transformation forms of the SOCCVI problem. Using the equivalent transformation forms and the properties of the projection operators, the augmented Lagrangian method can be established and its global convergence is proved. The inexact Newton method is used to solve the inner problems which arise from the augmented Lagrangian method for solving the numerical examples. Numerical results for three examples are reported to verify the effectiveness of the augmented Lagrangian method for obtaining approximate solutions.

Keywords: Second-order cone constrained variational inequalities; augmented Lagrangian method; inexact Newton method (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1142/S0217595922500300

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