We present data structures for maintaining the relative convex hull of a set of points (sites) in the presence of pairwise non-crossing line segments (barriers) that subdivide a bounding box into simply connected faces. Our data structures have O((n + m) log n) size for n sites and m barriers. They support O(m) barrier insertions and O(n) site deletions in O((m + n) polylog (mn)) total time, an...

We present a novel semi-supervised training algorithm for learning dependency parsers. By combining a supervised large margin loss with an unsupervised least squares loss, a discriminative, convex, semi-supervised learning algorithm can be obtained that is applicable to large-scale problems. To demonstrate the benefits of this approach, we apply the technique to learning dependency parsers from...

In this paper, we introduce three new types of generalized convex functions, called semi E-pseudoinvex, strictly semi Epseudoinvex and semi E-quasiinvex functions. Then some of their basic properties are studied, We used directional derivative and obtain the new results in this class of functions. As applications of our results, we obtain optimal solutions for multiobjective programming. AMS Su...