A Predictor-corrector algorithm with multiple corrections for convex quadratic programming

Authors:
Zhongyi Liu;Yue Chen;Wenyu Sun;Zhihui Wei
Affiliations:
College of Science, Hohai University, Nanjing, China 210098;Jincheng College, Nanjing University of Aeronautics and Astronautics, Nanjing, China 211156;School of Mathematical Science, Nanjing Normal University, Nanjing, China 210097;School of Computer Science and Technology, Nanjing University of Science and Technology, Nanjing, China 210094
Venue:
Computational Optimization and Applications
Year:
2012

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Abstract

Recently an infeasible interior-point algorithm for linear programming (LP) was presented by Liu and Sun. By using similar predictor steps, we give a (feasible) predictor-corrector algorithm for convex quadratic programming (QP). We introduce a (scaled) proximity measure and a dynamical forcing factor (centering parameter). The latter is used to force the duality gap to decrease. The algorithm can decrease the duality gap monotonically. Polynomial complexity can be proved and the result coincides with the best one for LP, namely, $O(\sqrt{n}\log n\mu^{0}/\varepsilon)$ .