caa a22 4500 463169689 CHVBK 20180406164809.0 cr unu---uuuuu 170326e20071201xx s 000 0 eng 10.1007/s10957-007-9220-2 doi (NATIONALLICENCE)springer-10.1007/s10957-007-9220-2 New Self-Concordant Barrier for the Hypercube [Elektronische Daten] [E. PapaQuiroz, P. Oliveira] We introduce a new barrier function to build new interior-point algorithms to solve optimization problems with bounded variables. First, we show that this function is a (3/2)n-self-concordant barrier for the unitary hypercube [0,1] n , assuring thus the polynomial property of related algorithms. Second, using the Hessian metric of that barrier, we present new explicit algorithms from the point of view of Riemannian geometry applications. Third, we prove that the central path defined by the new barrier to solve a certain class of linearly constrained convex problems maintains most of the properties of the central path defined by the usual logarithmic barrier. We present also a primal long-step path-following algorithm with similar complexity to the classical barrier. Finally, we introduce a new proximal-point Bregman type algorithm to solve linear problems in [0,1] n and prove its convergence. Springer Science+Business Media, LLC, 2007 Interior-point methods nationallicence Self-concordant barrier nationallicence Newton methods nationallicence Geodesic algorithms nationallicence Proximal-point algorithms nationallicence PapaQuiroz E. Department of Systems Engineering and Computer Sciences, PESC-COPPE, Federal University of Rio de Janeiro, Rio de Janeiro, Brazil aut Oliveira P. Department of Systems Engineering and Computer Sciences, PESC-COPPE, Federal University of Rio de Janeiro, Rio de Janeiro, Brazil aut Journal of Optimization Theory and Applications Springer US; http://www.springer-ny.com 135/3(2007-12-01), 475-490 0022-3239 135:3<475 2007 135 10957 https://doi.org/10.1007/s10957-007-9220-2 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10957-007-9220-2 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- PapaQuiroz E. Department of Systems Engineering and Computer Sciences, PESC-COPPE, Federal University of Rio de Janeiro, Rio de Janeiro, Brazil aut NATIONALLICENCE 700 1- Oliveira P. Department of Systems Engineering and Computer Sciences, PESC-COPPE, Federal University of Rio de Janeiro, Rio de Janeiro, Brazil aut NATIONALLICENCE 773 0- Journal of Optimization Theory and Applications Springer US; http://www.springer-ny.com 135/3(2007-12-01), 475-490 0022-3239 135:3<475 2007 135 10957 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer