Abstract
Traditional inexact SQP algorithm can only solve equality constrained optimization (Byrd et al. Math. Program. 122, 273–299 2010). In this paper, we propose a new inexact SQP algorithm with affine scaling technique for nonlinear systems of mixed equalities and inequalities, which arise in complementarity and variational inequalities. The nonlinear systems are transformed into a special nonlinear optimization with equality and bound constraints, and then we give a new inexact SQP algorithm for solving it. The new algorithm equipped with affine scaling technique does not require a quadratic programming subproblem with inequality constraints. The search direction is computed by solving one linear system approximately using iterative linear algebra techniques. Under mild assumptions, we discuss the global convergence. The preliminary numerical results show the effectiveness of the proposed algorithm.
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Acknowledgements
The authors gratefully acknowledge the Projects (No. 11201304, No. 11371253) supported by the National Natural Science Foundation of China, the Project supported by the Innovation Program of Shanghai Municipal Education Commission, the project sponsored by Natural Science Foundation of Shanghai.
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Gu, C., Zhu, D. & Pei, Y. A new inexact SQP algorithm for nonlinear systems of mixed equalities and inequalities. Numer Algor 78, 1233–1253 (2018). https://doi.org/10.1007/s11075-017-0421-y
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DOI: https://doi.org/10.1007/s11075-017-0421-y
Keywords
- Inexact SQP algorithm
- Affine scaling technique
- Complementarity
- Variational inequalities
- Dwindling filter method
- Convergence