Abstract
A trust region algorithm is proposed for solving bilevel programming problems where the lower lwel programming problem is a strongly convex programming problem with linear constraints. This algorithm is based on a trust region algorithm for nonsmooth unconstrained optimization problems, and its global convergence is also proved.
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References
Vincent, L. N., Calamai, P. H., Bilevel and multilevel programming: A bibliography review,Journal of Global Optimization. 1994. 3: 291.
Yuan, Y. X., Trust region algorithms for nonlinear programming,Computational Mathematics, 1994, 16: 205.
Dempe, S., On Generalized Differentiability of Optimal Solutions and its Application to an Algorithm for solving Bilevel Optimization Problems, inRecent Advances in Nonsmooth Optimization (eds. Du, D., Qi, L.). Womerssley, R., Singapore: World Scientific Publishing Co Pte Ltd., 1995, 36.
Lou, Z. Q., Pang, J. S., Ralph, D.et al., Exact penalization and stationarity conditions of mathematical programs with equilibrium constraints.Mathematical Programming. 1996. 75: 19.
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Liu, G., Han, J. & Wang, S. A trust region algorithm for bilevel programing problems. Chin. Sci. Bull. 43, 820–824 (1998). https://doi.org/10.1007/BF03182744
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DOI: https://doi.org/10.1007/BF03182744