Primal and dual convergence of a proximal point exponential penalty method for linear programming |
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Authors: | F Alvarez R Cominetti |
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Institution: | (1) Universidad de Chile, Departamento de Ingeniería Matemática and Centro de Modelamiento Matemático, Casilla 170/3, Correo 3, Santiago, Chile, CL |
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Abstract: | We consider the diagonal inexact proximal point iteration where f(x,r)=c
T
x+r∑exp(A
i
x-b
i
)/r] is the exponential penalty approximation of the linear program min{c
T
x:Ax≤b}. We prove that under an appropriate choice of the sequences λ
k
, ε
k
and with some control on the residual ν
k
, for every r
k
→0+ the sequence u
k
converges towards an optimal point u
∞ of the linear program. We also study the convergence of the associated dual sequence μ
i
k
=exp(A
i
u
k
-b
i
)/r
k
] towards a dual optimal solution.
Received: May 2000 / Accepted: November 2001?Published online June 25, 2002 |
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Keywords: | : proximal point – exponential penalty – linear programming |
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