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An L \infty/L 1-Constrained Quadratic Optimization Problem with Applications to Neural Networks

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Abstract

Pattern formation in associative neural networks is related to a quadratic optimization problem. Biological considerations imply that the functional is constrained in the L \infty norm and in the L 1 norm. We consider such optimization problems. We derive the Euler–Lagrange equations, and construct basic properties of the maximizers. We study in some detail the case where the kernel of the quadratic functional is finite-dimensional. In this case the optimization problem can be fully characterized by the geometry of a certain convex and compact finite-dimensional set.

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  1. Arie Leizarowitz

    Present address: Department of Mathematics, Technion, Haifa 32000, Israel

Authors and Affiliations

  1. Mathematics Department, Indiana University, Bloomington, IN 47405, USA

    Arie Leizarowitz & Jacob Rubinstein

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  1. Arie Leizarowitz
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  2. Jacob Rubinstein
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Correspondence to Arie Leizarowitz or Jacob Rubinstein.

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Leizarowitz, A., Rubinstein, J. An L \infty/L 1-Constrained Quadratic Optimization Problem with Applications to Neural Networks. Appl Math Optim 49, 55–80 (2004). https://doi.org/10.1007/s00245-003-0780-8

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  • DOI: https://doi.org/10.1007/s00245-003-0780-8

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