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Some notes on the quasi-Newton methods

Masanori Ozawa, Hiroshi Yanai (1982)

Aplikace matematiky

A survey note whose aim is to establish the heuristics and natural relations in a class of Quasi-Newton methods in optimization problems. It is shown that a particular algorithm of the class is specified by characcterizing some parameters (scalars and matrices) in a general solution of a matrix equation.

Some remarks on the space of differences of sublinear functions

Sven Bartels, Diethard Pallaschke (1994)

Applicationes Mathematicae

Two properties concerning the space of differences of sublinear functions D(X) for a real Banach space X are proved. First, we show that for a real separable Banach space (X,‖·‖) there exists a countable family of seminorms such that D(X) becomes a Fréchet space. For X = ℝ^n this construction yields a norm such that D(ℝ^n) becomes a Banach space. Furthermore, we show that for a real Banach space with a smooth dual every sublinear Lipschitzian function can be expressed by the Fenchel conjugate of...

Some scheduling problems with past sequence dependent setup times under the effects of nonlinear deterioration and time-dependent learning

M. Duran Toksarı, Daniel Oron, Ertan Güner (2010)

RAIRO - Operations Research

This paper studies scheduling problems which include a combination of nonlinear job deterioration and a time-dependent learning effect. We use past sequence dependent (p-s-d) setup times, which is first introduced by Koulamas and Kyparisis [Eur. J. Oper. Res.187 (2008) 1045–1049]. They considered a new form of setup times which depend on all already scheduled jobs from the current batch. Job deterioration and learning co-exist in various real life scheduling settings. By the effects of learning...

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