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A strongly and superlinearly convergent SQP algorithm for optimization problems with linear complementarity constraints. (English) Zbl 1136.90514
Summary: This paper discusses a kind of optimization problem with linear complementarity constraints, and presents a sequential quadratic programming (SQP) algorithm for solving a stationary point of the problem. The algorithm is a modification of the SQP algorithm proposed by M. Fukushima et al. [Comput. Optim. Appl. 10, No. 1, 5–34 (1998; Zbl 0904.90153)], and is based on a reformulation of complementarity condition as a system of linear equations. At each iteration, one quadratic programming and one system of equations needs to be solved, and a curve search is used to yield the step size. Under some appropriate assumptions, including the lower-level strict complementarity, but without the upper-level strict complementarity for the inequality constraints, the algorithm is proved to possess strong convergence and superlinear convergence. Some preliminary numerical results are reported.

MSC:
90C55 Methods of successive quadratic programming type
90C33 Complementarity and equilibrium problems and variational inequalities (finite dimensions) (aspects of mathematical programming)
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