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Multi-Standard Quadratic Optimization: interior point methods and cone programming reformulation

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Abstract

A Standard Quadratic Optimization Problem (StQP) consists of maximizing a (possibly indefinite) quadratic form over the standard simplex. Likewise, in a multi-StQP we have to maximize a (possibly indefinite) quadratic form over the Cartesian product of several standard simplices (of possibly different dimensions). Among many other applications, multi-StQPs occur in Machine Learning Problems. Several converging monotone interior point methods are established, which differ from the usual ones used in cone programming. Further, we prove an exact cone programming reformulation for establishing rigorous yet affordable bounds and finding improving directions.

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Authors and Affiliations

  1. Dept. of Statistics and Decision Support Systems, University of Vienna, Brünnerstr. 72, 1210, Vienna, Austria

    Immanuel M. Bomze & Werner Schachinger

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  1. Immanuel M. Bomze
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  2. Werner Schachinger
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Correspondence to Immanuel M. Bomze.

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Paper presented at the 46th Erice Workshop: New Problems and Innovative Methods in Nonlinear Optimization, July 31–August 9, 2007.

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Bomze, I.M., Schachinger, W. Multi-Standard Quadratic Optimization: interior point methods and cone programming reformulation. Comput Optim Appl 45, 237–256 (2010). https://doi.org/10.1007/s10589-009-9243-8

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  • DOI: https://doi.org/10.1007/s10589-009-9243-8

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