A relaxed sequence quadratic programming method for solving bilevel programming problems
This article considers a class of bilevel programming problems with a special structure,where the lower-level problems are convex problems.First,the constraint function of the lower-level problem is penalized to the objective function by the interior point penalty method,so that the lower-level problem is approximated as a series of unconstrained optimiza-tion problems.Then the optimal set of solutions of the unconstrained lower-level problems is replaced by the KKT condition,and then the bilevel programming problem is approximated by a series of relaxed single-level problems.This article designs a smooth sequential quadratic programming algorithm to solve the relaxation problem and show that the iteration sequence generated by the algorithm converges to the weakly stationary point of the bilevel program-ming problem when the penalty factor converges to zero.The numerical experiments verify the feasibility of the algorithm.
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