 |
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| Volume 3, Number 1, January 2007, pp. 53-72 | |||||||||
|
Katrin Hauk and Florian Jarre |
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| Key words: | |||||||||
| linear program, piecewise quadratic function, augmented Lagrangian | |||||||||
| Mathematices Subject Classification: 90C05 | |||||||||
| References | |||||||||
|
|||||||||
| Volume 3, Number 1, January 2007, pp. 53-72 | |||||||||
|
Katrin Hauk and Florian Jarre |
|||||||||
| Key words: | |||||||||
| linear program, piecewise quadratic function, augmented Lagrangian | |||||||||
| Mathematices Subject Classification: 90C05 | |||||||||
| References | |||||||||
|
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| Abstract: | |||
| This paper explores the solution of linear programs based on the minimization of convex, differentiable, piecewise quadratic functions. These functions define certain implicit functions which provide bounds for a complexity analysis. One of the approaches is based on an augmented Lagrangian method. The results that are known for the augmented Lagrangian in the case of more general nonlinear programs are strengthened and a link between linear programs and convex conjugates of convex piecewise quadratic functions is established. | |||
| Linear programs and implicit functions |
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