This paper introduces the generalized forward-backward splitting algorithm for minimizing convex functions of the form F + ∑i=1Gi, where F has a Lipschitzcontinuous gradient and the Gi’s are simple in the sense that their Moreau proximity operators are easy to compute. While the forward-backward algorithm cannot deal with more than n = 1 non-smooth function, our method generalizes it to the cas...

A smooth, projective surface S of general type is said to be a standard isotrivial fibration if there exist a finite group G acting faithfully on two smooth projective curves C and F so that S is isomorphic to the minimal desingularization of T := (C × F)/G. If T is smooth then S = T is called a quasi-bundle. In this paper we classify the standard isotrivial fibrations with pg = q = 1 which are...

Title of Dissertation: Nonparametric Quasi-likelihood in Longitudinal Data Analysis Xiaoping Jiang, Doctor of Philosophy, 2004 Dissertation directed by: Professor Paul J. Smith Statistics Program Department of Mathematics This dissertation proposes a nonparametric quasi-likelihood approach to estimate regression coefficients in the class of generalized linear regression models for longitudinal ...

The spectral sequence predicted by A. Beilinson relating motivic cohomology to algebraic K-theory has been established for smooth quasi-projective varieties over a field (cf. [FS], [L1]). Among other properties verified, this spectral sequence has the expected multiplicative behavior (involving cup product in motivic cohomology and product in algebraic K-theory) and a good multiplicative “mod-n...

A smooth, projective surface S of general type is said to be a standard isotrivial fibration if there exist a finite group G which acts faithfully on two smooth projective curves C and F so that S is isomorphic to the minimal desingularization of T := (C × F)/G. If T is smooth then S = T is called a quasi-bundle. In this paper we classify the standard isotrivial fibrations with pg = q = 1 which...

The Schatten quasi-norm can be used to bridge the gap between the nuclear norm and rank function. However, most existing algorithms are too slow or even impractical for large-scale problems, due to the singular value decomposition (SVD) or eigenvalue decomposition (EVD) of the whole matrix in each iteration. In this paper, we rigorously prove that for any 0< p≤ 1, p1, p2 > 0 satisfying 1/p= 1/p...

We analyze a quasi-Monte Carlo method to solve the initial-value problem for a system of differential equations y′(t) = f(t, y(t)). The function f is smooth in y and we suppose that f and D1 yf are of bounded variation in t and that D2 yf is bounded in a neighborhood of the graph of the solution. The method is akin to the second order Heun method of the Runge-Kutta family. It uses a quasi-Monte...