Applied Mathematics and Optimization

, Volume 49, Issue 1, pp 55–80 | Cite as

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

  • Arie Leizarowitz
  • Jacob Rubinstein


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.

Quadratic optimization Neural networks 


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Copyright information

© Springer-Verlag 2003

Authors and Affiliations

  1. 1.Mathematics Department, Indiana University, Bloomington, IN 47405USA
  2. 2.Department of Mathematics, Technion, Haifa 32000Israel

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