We investigate the problem of scheduling n jobs in s-stage hybrid flowshops with parallel identical machines at each stage. The objective is to find a schedule that minimizes the sum of weighted completion times of the jobs. This problem has been proven to be NP-hard. In this paper, an integer programming formulation is constructed for the problem. A new Lagrangian relaxation algorithm is prese...

We generalize the method of [Bo03] to prove a version of the converse theorem of JacquetLanglands with relaxed conditions on the twists by ramified idèle class characters.

Given a bounded open set Ω ⊂ ℝ 2 , we study the relaxation of nonparametric area functional in strict topology BV (Ω; ). and compute it for vortex-type maps, more generally maps W 1,1 (Ω;S 1 ) having finite number topological singularities. We also extend analysis to some specific piecewise constant ), including symmetric triple junction map.

This paper presents a newmodel of support vector machines (SVMs) that handle data with tolerance and uncertainty. The constraints of the SVM are converted to fuzzy inequality. Giving more relaxation to the constraints allows us to consider an importance degree for each training samples in the constraints of the SVM. The new method is called relaxed constraints support vector machines (RSVMs). A...