An extension of proximal methods for quasiconvex minimization on the nonnegative orthant

An extension of proximal methods for quasiconvex minimization on the nonnegative orthant

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Article ID: iaor20119354
Volume: 216
Issue: 1
Start Page Number: 26
End Page Number: 32
Publication Date: Jan 2012
Journal: European Journal of Operational Research
Authors: ,
Keywords: iterative methods, proximal point algorithm
Abstract:

In this paper we propose an extension of proximal methods to solve minimization problems with quasiconvex objective functions on the nonnegative orthant. Assuming that the function is bounded from below and lower semicontinuous and using a general proximal distance, it is proved that the iterations given by our algorithm are well defined and stay in the positive orthant. If the objective function is quasiconvex we obtain the convergence of the iterates to a certain set which contains the set of optimal solutions and convergence to a KKT point if the function is continuously differentiable and the proximal parameters are bounded. Furthermore, we introduce a sufficient condition on the proximal distance such that the sequence converges to an optimal solution of the problem.

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