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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...

Spatially-distributed coverage optimization and control with limited-range interactions

Jorge Cortés, Sonia Martínez, Francesco Bullo (2005)

ESAIM: Control, Optimisation and Calculus of Variations

This paper presents coordination algorithms for groups of mobile agents performing deployment and coverage tasks. As an important modeling constraint, we assume that each mobile agent has a limited sensing or communication radius. Based on the geometry of Voronoi partitions and proximity graphs, we analyze a class of aggregate objective functions and propose coverage algorithms in continuous and discrete time. These algorithms have convergence guarantees and are spatially distributed with respect...

Spatially-distributed coverage optimization and control with limited-range interactions

Jorge Cortés, Sonia Martínez, Francesco Bullo (2010)

ESAIM: Control, Optimisation and Calculus of Variations

This paper presents coordination algorithms for groups of mobile agents performing deployment and coverage tasks. As an important modeling constraint, we assume that each mobile agent has a limited sensing or communication radius.
Based on the geometry of Voronoi partitions and proximity graphs, we analyze a class of aggregate objective functions and propose coverage algorithms in continuous and discrete time.
These algorithms have convergence guarantees and are spatially distributed with...

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