Abstract
To minimize a convex function f, we state a penalty-type bundle algorithm, where the penalty uses a variable metric. This metric is updated according to quasi-Newton formulae based on Moreau-Yosida approximations of f. In particular, we introduce a “reversal” quasi-Newton formula, specially suited for our purpose. We consider several variants in the algorithm and discuss their respective merits. Furthermore, we accept a degenerate penalty term in the Moreau-Yosida regularization.
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References
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© 1994 Springer-Verlag
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Lemaréchal, C., Sagastizábal, C. (1994). An approach to variable metric bundle methods. In: Henry, J., Yvon, JP. (eds) System Modelling and Optimization. Lecture Notes in Control and Information Sciences, vol 197. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0035464
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DOI: https://doi.org/10.1007/BFb0035464
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