caa a22 4500 463169824 CHVBK 20180406164810.0 cr unu---uuuuu 170326e20070101xx s 000 0 eng 10.1007/s10957-006-9095-7 doi (NATIONALLICENCE)springer-10.1007/s10957-006-9095-7 Adaptive Large-Neighborhood Self-Regular Predictor-Corrector Interior-Point Methods for Linear Optimization [Elektronische Daten] [M. Salahi, T. Terlaky] It is known that predictor-corrector methods in a large neighborhood of the central path are among the most efficient interior-point methods (IPMs) for linear optimization (LO) problems. The best iteration bound based on the classical logarithmic barrier function is O(nlog (n/∊)). In this paper, we propose a family of self-regular proximity-based predictor-corrector (SRPC) IPMs for LO in a large neighborhood of the central path. In the predictor step, we use either an affine scaling or a self-regular direction; in the corrector step, we use always a self-regular direction. Our new algorithms use a special proximity function with different search directions and thus allows us to improve the so far best theoretical iteration complexity for a family of SRPC IPMs. An O $$(\sqrt{n}{\exp} ((1 - q + {\log} n)/2) {\log} n {\log} (n/\epsilon))$$ worst-case iteration bound with quadratic convergence is established, where q is the barrier degree of the SR proximity function. Springer Science+Business Media, Inc., 2007 Linear optimization nationallicence predictor-corrector methods nationallicence quadratic convergence nationallicence self-regular proximity functions nationallicence polynomial complexity nationallicence Salahi M. Advanced Optimization Laboratory, Department of Computing and Software, McMaster University, Hamilton, Ontario, Canada aut Terlaky T. Advanced Optimization Laboratory, Department of Computing and Software, McMaster University, Hamilton, Ontario, Canada aut Journal of Optimization Theory and Applications Kluwer Academic Publishers-Plenum Publishers; http://www.springer-ny.com 132/1(2007-01-01), 143-160 0022-3239 132:1<143 2007 132 10957 https://doi.org/10.1007/s10957-006-9095-7 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10957-006-9095-7 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Salahi M. Advanced Optimization Laboratory, Department of Computing and Software, McMaster University, Hamilton, Ontario, Canada aut NATIONALLICENCE 700 1- Terlaky T. Advanced Optimization Laboratory, Department of Computing and Software, McMaster University, Hamilton, Ontario, Canada aut NATIONALLICENCE 773 0- Journal of Optimization Theory and Applications Kluwer Academic Publishers-Plenum Publishers; http://www.springer-ny.com 132/1(2007-01-01), 143-160 0022-3239 132:1<143 2007 132 10957 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer