in this paper, we study the problem of minimizing the ratio of two quadratic functions subject to a quadratic constraint. first we introduce a parametric equivalent of the problem. then a bisection and a generalized newton-based method algorithms are presented to solve it. in order to solve the quadratically constrained quadratic minimization problem within both algorithms, a semidefinite optim...

We study the regularization and renormalization of the Yang-Mills theory in the framework of the manifestly invariant formalism, which consists of a higher covariant derivative with an infinitely many PauliVillars fields. Unphysical logarithmic divergence, which is the problematic point on the Slavnov’s method, does not appear in our scheme, and the well-known vale of the renormalization group ...

In this paper, we consider the problem of minimizing a continuously differentiable function on Stiefel manifold. To solve problem, develop geodesic-free proximal point algorithm equipped with Euclidean distance that does not require use Riemannian metric. The proposed method can be regarded as an iterative fixed-point repeatedly applies operator to initial point. addition, establish global conv...

When solving a quadratic program (QP), one can improve the numerical stability of any QP solver by performing proximal-point outer iterations, resulting in sequence better conditioned QPs. In this letter we present method which, for given multi-parametric (mpQP) and polyhedral set parameters, determines which sequences QPs will have to be solved when using iterations. By knowing sequence, bound...

Novelty is an important psychological construct that affects both perceptual and behavioral processes. Here, we propose a lexical novelty score (LNS) for a song’s lyric, based on the statistical properties of a corpus of 275,905 lyrics (available at www.smcnus.org/lyrics/). A lyric-level LNS was derived as a function of the inverse document frequencies of its unique words. An artist-level LNS w...

In this paper, we propose a stochastic proximal gradient method to train ternary weight neural networks (TNN). The proposed method features weight ternarization via an exact formula of proximal operator. Our experiments show that our trained TNN are able to preserve the state-of-the-art performance on MNIST and CIFAR-10 benchmark datesets.

Abstract We present a new variant of the Chambolle–Pock primal–dual algorithm with Bregman distances, analyze its convergence, and apply it to centering problem in sparse semidefinite programming. The novelty method is line search procedure for selecting suitable step sizes. obviates need estimating norm constraint matrix strong convexity constant kernel. As an application, we discuss large-sca...