In general, the set of users utilities is bounded because of the limitation of resources. There may exist many Pareto optimal points in the set of users utilities. For selecting a Pareto optimum point, a family of fairness criteria, that contains the max-min fairness and a parameterized family of fairness (by Mo and Walrand), has been proposed and examined in some concrete networking contexts t...

Sinkhorn divergence is a symmetric normalization of entropic regularized optimal transport. It smooth and continuous metrized weak-convergence with excellent geometric properties. We use it as an alternative for the minimax objective function in formulating generative adversarial networks. The optimization defined objective, under non-convex non-concave condition. This work focuses on optimizat...

Let X be a Hilbert space and let Cn, n = 1, . . . ,N be convex closed subsets of X . The convex feasibility problem is to find some point x ∈ N ⋂ n=1 Cn, when this intersection is non-empty. In this talk we discuss projection algorithms for finding such a feasibility point. These algorithms have wide ranging applications including: solutions to convex inequalities, minimization of convex nonsmo...

The dichromatic reflectance model introduced by Shafer [16] predicts that the colour signals of most materials fall on a plane spanned by a vector due to the material and a vector that represents the scene illuminant. Since the illuminant is in the span of all dichromatic planes, colour constancy can be achieved by finding the intersection of two or more planes. Unfortunately, this approach has...

In this paper, we study a new problem of finding a convex drawing of graphs with a non-convex boundary. It is proved that every triconnected plane graph whose boundary is fixed with a star-shaped polygon admits a drawing in which every inner facial cycle is drawn as a convex polygon. Such a drawing, called an inner-convex drawing, can be obtained in linear time.