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A New Class of Interior Proximal Methods for Optimization over the Positive Orthant ∗

By Sissy Da, Silva Souza and Paulo Roberto Oliveira


Abstract. In this work we present a family of interior proximal methods with variable metric for solving convex optimization problems under nonnegativity contraints. We propose an algorithm whose kernels are metrics generated by diagonal matrices updated in each step and the regularization parameters are conveniently determinated in each iteration to force the iterates to be interior points. We show the well definedness of the algorithm, and we establish weak convergence to the solution set of the problem, in the sense that the sequence of the iterates is bounded, the difference between the successive iterates converges to zero and any limit point is a solution to the problem. We also propose an inexact algorithm and we obtain the same convergence result than that proved in the exact case

Topics: interior point algorithms, proximal methods, variable metric, optimization problems
Year: 2006
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