caa a22 4500 463169581 CHVBK 20180406164809.0 cr unu---uuuuu 170326e20071201xx s 000 0 eng 10.1007/s10957-007-9281-2 doi (NATIONALLICENCE)springer-10.1007/s10957-007-9281-2 Approximate Duality [Elektronische Daten] [C. Scovel, D. Hush, I. Steinwart] We extend the Lagrangian duality theory for convex optimization problems to incorporate approximate solutions. In particular, we generalize well-known relationships between minimizers of a convex optimization problem, maximizers of its Lagrangian dual, saddle points of the Lagrangian, Kuhn-Tucker vectors, and Kuhn-Tucker conditions to incorporate approximate versions. As an application, we show how the theory can be used for convex quadratic programming and then apply the results to support vector machines from learning theory. Springer Science+Business Media, LLC, 2007 Lagrangian duality nationallicence Approximations nationallicence Saddle points nationallicence Kuhn-Tucker conditions nationallicence Support vector machines nationallicence Scovel C. Modeling, Algorithms, and Informatics Group, Los Alamos National Laboratory, Los Alamos, NM, USA aut Hush D. Modeling, Algorithms, and Informatics Group, Los Alamos National Laboratory, Los Alamos, NM, USA aut Steinwart I. Modeling, Algorithms, and Informatics Group, Los Alamos National Laboratory, Los Alamos, NM, USA aut Journal of Optimization Theory and Applications Springer US; http://www.springer-ny.com 135/3(2007-12-01), 429-443 0022-3239 135:3<429 2007 135 10957 https://doi.org/10.1007/s10957-007-9281-2 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10957-007-9281-2 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Scovel C. Modeling, Algorithms, and Informatics Group, Los Alamos National Laboratory, Los Alamos, NM, USA aut NATIONALLICENCE 700 1- Hush D. Modeling, Algorithms, and Informatics Group, Los Alamos National Laboratory, Los Alamos, NM, USA aut NATIONALLICENCE 700 1- Steinwart I. Modeling, Algorithms, and Informatics Group, Los Alamos National Laboratory, Los Alamos, NM, USA aut NATIONALLICENCE 773 0- Journal of Optimization Theory and Applications Springer US; http://www.springer-ny.com 135/3(2007-12-01), 429-443 0022-3239 135:3<429 2007 135 10957 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer