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

An L \infty / L 1 -Constrained Quadratic Optimization Problem with Applications to Neural Networks 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Applied Mathematics and Optimization Springer Journals

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

, Volume 49 (1) – Dec 1, 2004
26 pages

Publisher
Springer-Verlag
Subject
Mathematics; Calculus of Variations and Optimal Control; Optimization; Systems Theory, Control; Mathematical and Computational Physics; Mathematical Methods in Physics; Numerical and Computational Methods
ISSN
0095-4616
eISSN
1432-0606
D.O.I.
10.1007/s00245-003-0780-8
Publisher site
See Article on Publisher Site

### 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.

### Journal

Applied Mathematics and OptimizationSpringer Journals

Published: Dec 1, 2004

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