Asymptotic analysis of the exponential penalty trajectory in linear programming

R. Cominetti, J. San Martín

Producción científica: Contribución a una revistaArtículorevisión exhaustiva

59 Citas (Scopus)

Resumen

We consider the linear program min{c′x: Ax≤b} and the associated exponential penalty function fr(x) = c′x + rΣexp[(Aix - bi)/r]. For r close to 0, the unconstrained minimizer x(r) of fr admits an asymptotic expansion of the form x(r) = x* + rd* + η(r) where x* is a particular optimal solution of the linear program and the error term η(r) has an exponentially fast decay. Using duality theory we exhibit an associated dual trajectory λ(r) which converges exponentially fast to a particular dual optimal solution. These results are completed by an asymptotic analysis when r tends to ∞: the primal trajectory has an asymptotic ray and the dual trajectory converges to an interior dual feasible solution.

Idioma originalInglés
Páginas (desde-hasta)169-187
Número de páginas19
PublicaciónMathematical Programming
Volumen67
N.º1-3
DOI
EstadoPublicada - oct. 1994

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