We present a novel method for dynamically deciding when, how, and to what extent soft constraints should be relaxed. The rst part of the method is a depth-rst search and best-rst repair algorithm, and the second part of the method is an algorithm for gradually relaxing soft constraints. The method can guarantee that (1) a soft constraint will be relaxed only when no backtrack (repair) can be ma...

The main purpose of this paper is to study the relationship between those functions that aggregate relaxed indistinguishability fuzzy relations with respect a collection t-norms and merge pseudo-metrics, extending classical approach explored for pseudo-metrics relations. Special attention paid distinguished class SSI-relaxed showing merging special type can be expressed through aggregating SSD-...

We describe an electoral system for distributing seats in a parliament. It gives proportionality for the political parties and close to proportionality for constituencies. The system suggested here is a version of the system used in Sweden and other Nordic countries with permanent seats in each constituency and adjustment seats to give proportionality on the national level. In the national elec...

The negative gradient direction to find local minimizers has been associated with the classical steepest descent method which behaves poorly except for very well conditioned problems. We stress out that the poor behavior of the steepest descent methods is due to the optimal Cauchy choice of steplength and not to the choice of the search direction. We discuss over and under relaxation of the opt...

The Traveling Tournament Problem (TTP) is a sports scheduling problem that includes two major issues in creating timetables: home/away pattern feasibility and travel distance. In this problem, the schedule must be compact: every team plays in every time slot. However, there are some sports leagues that have both home/away pattern restrictions and distance limits, but do not require a compact sc...

The notions of relaxed submonotone and relaxed monotone mappings in Banach spaces are introduced and many of their properties are investigated. For example, the Clarke subdifferential of a locally Lipschitz function in a separable Banach space is relaxed submonotone on a residual subset. For example, it is shown that this property need not be valid on the whole space. We prove, under certain hy...

We use the Margin Infused Relaxed Algorithm of Crammer et al. to add a large number of new features to two machine translation systems: the Hiero hierarchical phrasebased translation system and our syntax-based translation system. On a large-scale ChineseEnglish translation task, we obtain statistically significant improvements of +1.5 B and +1.1 B, respectively. We analyze the impact of ...