In this paper, we study the low-rank matrix minimization problem, where loss function is convex but nonsmooth and penalty term defined by cardinality function. We first introduce an exact continuous relaxation, that is, both problems have same minimizers optimal value. particular, a class of lifted stationary points relaxed problem show any local minimizer must be point. addition, derive lower ...

An evolutionary algorithm that utilizes a-priori problem specific information and allows intuitive representation of the problem design variables is proposed. A technique for conditioning the components of the fitness statement using ranking and a graphical method for monitoring components of the rank based fitness function are presented. By utilizing generationally dependant non-linear rank ba...

In Rank-aware query processing, reverse rank queries have already attracted significant interests. Reverse rank queries can find matching customers for a given product based on individual customers’ preference. The results are used in numerous real-life applications, such as market analysis and product placement. Efficient processing of reverse rank queries is challenging because it needs to co...

How to rank Web resources is critical to Web Resource Discovery (Search Engine). This paper not only points out the weakness of current approaches, but also presents in-depth analysis of the multidimensionality and subjectivity of rank algorithms. From a dynamics viewpoint, this paper abstracts a user’s Web surfing action as a Markov model. Based on this model, we propose a new rank algorithm. ...