TY - JOUR

T1 - Entropic proximal decomposition methods for convex programs and variational inequalities

AU - Auslander, Alfred

AU - Teboulle, Marc

PY - 2001/10

Y1 - 2001/10

N2 - We consider convex optimization and variational inequality problems with a given separable structure. We propose a new decomposition method for these problems which combines the recent logarithmic-quadratic proximal theory introduced by the authors with a decomposition method given by Chen-Teboulle for convex problems with particular structure. The resulting method allows to produce for the first time provably convergent decomposition schemes based on C∞ Lagrangians for solving convex structured problems. Under the only assumption that the primal-dual problems have nonempty solution sets, global convergence of the primal-dual sequences produced by the algorithm is established.

AB - We consider convex optimization and variational inequality problems with a given separable structure. We propose a new decomposition method for these problems which combines the recent logarithmic-quadratic proximal theory introduced by the authors with a decomposition method given by Chen-Teboulle for convex problems with particular structure. The resulting method allows to produce for the first time provably convergent decomposition schemes based on C∞ Lagrangians for solving convex structured problems. Under the only assumption that the primal-dual problems have nonempty solution sets, global convergence of the primal-dual sequences produced by the algorithm is established.

KW - Convex optimization

KW - Decomposition methods

KW - Entropic/interior proximal methods

KW - Lagrangian multiplier methods

KW - Variational inequalities

UR - http://www.scopus.com/inward/record.url?scp=4043138107&partnerID=8YFLogxK

U2 - 10.1007/s101070100241

DO - 10.1007/s101070100241

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AN - SCOPUS:4043138107

VL - 91

SP - 33

EP - 47

JO - Mathematical Programming

JF - Mathematical Programming

SN - 0025-5610

IS - 1

ER -