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Digital Object Identifier (DOI) 10.1007/s10107-002-0295-0 Math. Program., Ser. A 93: 8796 (2002)

Summary: Digital Object Identifier (DOI) 10.1007/s10107-002-0295-0
Math. Program., Ser. A 93: 87­96 (2002)
F. Alvarez ˇ R. Cominetti
Primal and dual convergence of a proximal point
exponential penalty method for linear programming
Received: May 2000 / Accepted: November 2001
Published online June 25, 2002 ­ Springer-Verlag 2002
Abstract. We consider the diagonal inexact proximal point iteration
uk - uk-1
-k f uk,rk + k
where f(x,r) = cT
x +r exp[(Ai x - bi)/r] is the exponential penalty approximation of the linear program
x : Ax b}. We prove that under an appropriate choice of the sequences k, k and with some control
on the residual k, for every rk 0+ the sequence uk converges towards an optimal point u of the linear
program. We also study the convergence of the associated dual sequence ľk
i = exp[(Aiuk - bi)/rk] towards
a dual optimal solution.
Key words. proximal point ­ exponential penalty ­ linear programming


Source: Alvarez, Felipe - Departamento de Ingeniería Matemática, Universidad de Chile


Collections: Mathematics; Engineering