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A superlinearly convergent wide-neighborhood predictor-corrector interior-point algorithm for linear programming. (English) Zbl 1374.90378
Summary: In this paper we propose a new predictor-corrector algorithm with superlinear convergence in a wide neighborhood for linear programming problems. We let the centering parameter in a predictor step is chosen adaptively, which is different from other algorithms in the same wide neighborhood. The choice is a key for the local convergence of the new algorithm. In addition, we use the classical affine scaling direction as a part in a corrector step, not in a predictor step, which contributes to the complexity result. We prove that the new algorithm has a polynomial complexity of \(O(\sqrt{n}L)\), and the duality gap sequence is superlinearly convergent to zero, under the assumption that the iterate points sequence is convergent. Finally, numerical tests indicate its effectiveness.

90C33 Complementarity and equilibrium problems and variational inequalities (finite dimensions) (aspects of mathematical programming)
49M15 Newton-type methods
65K15 Numerical methods for variational inequalities and related problems
Full Text: DOI
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