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\iteman{io-port 05996139}
\itemau{Da Cruz Neto, J.X.; Lopes, J.O.; Travaglia, M.V.}
\itemti{Algorithms for quasiconvex minimization.}
\itemso{Optimization 60, No. 7-9, 1105-1117 (2011).}
\itemab
Summary: In this article we propose two algorithms for minimization of quasiconvex functions. The first one is of type subgradient. In the second one, we consider the steepest descent method with Armijo's rule. In both, we use elements from Plastria's lower subdifferential. Under certain conditions, we prove that the sequence generated by these algorithms globally converges to a solution. We provide a counter-example showing that the choice of the minus gradient direction does not assure the global convergence of the descent method to a solution. This counter-example is related to a mistake in the proof of the Theorem 3.1 of [{\it J. P. Dussault}, J. Optimization Theory Appl. 104, No. 3, 739--745 (2000; Zbl 0974.90018)]. We also point out the mistake in the proof of that theorem.
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\itemcc{}
\itemut{quasiconvex minimization; subgradient method; steepest descent method; abstract subdifferential}
\itemli{doi:10.1080/02331934.2010.528760}
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