2008 OCT 20 - (VerticalNews.com) -- "We analyze the problem of finding a point strictly interior to a bounded, convex, and fully dimensional set from a finite dimensional Hilbert space. We generalize the results obtained for the linear programming ( LP), semide finite programming (SDP), and second-order core programming (SOCP) cases," investigators in the United States report.

  "The cuts added by our algorithm are central and conic. In our analysis, we find an upper bound for the number of Newton steps required to compute an approximate analytic center. Also, we provide an upper bound for the total number of cuts added to solve the problem," wrote V.L. Basescu and colleagues ...read more

  2008 OCT 20 - (VerticalNews.com) -- According to recent research from Prague, Czech Republic, "Learning from data under constraints on model complexity is studied in terms of rates of approximate minimization of the regularized expected error functional."

  "For kernel models with an increasing number n of kernel functions, upper bounds on such rates are derived. The bounds are of the form a/n+b/root n, where a and b depend on the regularization parameter and on properties of the kernel, and of the probability measure de. ning the expected error," wrote V. Kurkova and colleagues ...read more

  2008 OCT 20 - (VerticalNews.com) -- According to a study from the United States, "We propose a new solution method for optimal stopping problems with random discounting for linear diffusions whose state space has a combination of natural, absorbing, or reflecting boundaries. The method uses a concave characterization of excessive functions for linear diffusions killed at a rate determined by a Markov additive functional and reduces the original problem to an undiscounted optimal stopping problem for a standard Brownian motion. ...read more