Approximate Duality

C. Scovel (), D. Hush and I. Steinwart
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C. Scovel: Los Alamos National Laboratory
D. Hush: Los Alamos National Laboratory
I. Steinwart: Los Alamos National Laboratory

Journal of Optimization Theory and Applications, 2007, vol. 135, issue 3, No 9, 429-443

Abstract: Abstract 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.

Keywords: Lagrangian duality; Approximations; Saddle points; Kuhn–Tucker conditions; Support vector machines (search for similar items in EconPapers)
Date: 2007
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DOI: 10.1007/s10957-007-9281-2

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