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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.

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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