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We present an inexact interior point proximal method to solve
linearly constrained convex problems. In fact, we derive a
primal-dual algorithm to solve the KKT conditions of the
optimization problem using a modified version of the rescaled
proximal method. We also present a pure primal method.
The proposed proximal method has as distinctive feature the
possibility of allowing inexact inner steps even for Linear
Programming. This is achieved by using an error criterion that
bounds the subgradient...
Proximal Point Methods (PPM) can be traced to the pioneer works of Moreau [16], Martinet [14,
15] and Rockafellar [19, 20] who used as regularization function the square of the Euclidean
norm. In this work, we study PPM in the context of optimization and we derive a class of such
methods which contains Rockafellar's result. We also present a less stringent criterion to the
acceptance of an approximate solution to the subproblems that arise in the inner loops of PPM.
Moreover, we introduce a new...
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