Abstract
In this paper, following the method of replacing the lower level problem with its Kuhn-Tucker optimality condition, we transform the nonlinear bilevel programming problem into a normal nonlinear programming problem with the complementary slackness constraint condition. Then, we get the penalized problem of the normal nonlinear programming problem by appending the complementary slackness condition to the upper level objective with a penalty. We prove that this penalty function is exact and the penalized problem and the nonlinear bilevel programming problem have the same global optimal solution set. Finally, we propose an algorithm for the nonlinear bilevel programming problem. The numerical results show that the algorithm is feasible and efficient.
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Foundation item: Supported by the Key Project on Science and Technology of Hubei Provincial Department of Education (D20103001)
Biography: PAN Qingfei, male, Associate professor, research direction: optimization theory and methods.
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Pan, Q., An, Z. & Qi, H. Exact penalty method for the nonlinear bilevel programming problem. Wuhan Univ. J. Nat. Sci. 15, 471–475 (2010). https://doi.org/10.1007/s11859-010-0686-7
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DOI: https://doi.org/10.1007/s11859-010-0686-7
Key words
- convex-quadratic programming
- nonlinear bilevel programming
- Kuhn-Tucker optimality condition
- penalty function method
- optimal solution