The reaction path is an important concept of theoretical chemistry. We discuss the definition with the help of diverse projection operators for the intrinsic reaction coordinate (IRC), for the following of the reduced gradient (RGF) or Newton trajectory (NT), and for the Gradient Extremal (GE). We describe different numerical schemes for the definitions in the context of string methods. It come...

Traditionally variational level set model for image segmentation is solved by using gradient descent method, which has low computational efficiency and needs complex re-initialization of level set functions as signed distance functions. In this paper, we first reformulate the variational model as a constrained optimization problem. Then we present an augmented Lagrangian projection method to pr...

We propose a supervised and localized dimensionality reduction method that combines multiple feature representations or kernels. Each feature representation or kernel is used where it is suitable through a parametric gating model in a supervised manner for efficient dimensionality reduction and classification, and local projection matrices are learned for each feature representation or kernel. ...

An electron spin resonance (ESR) imaging system, capable of acquiring three-dimensional (3D) images with a resolution of ,10310330 mm in a few minutes of acquisition, is presented. This ESR microscope employs a commercial continuous wave ESR spectrometer, working at 9.1 GHz, in conjunction with a miniature imaging probe (resonator+gradient coils), gradient current drivers, and control software....

We motivate this study from a recent work on a stochastic gradient descent (SGD) method with only one projection (Mahdavi et al., 2012), which aims at alleviating the computational bottleneck of the standard SGD method in performing the projection at each iteration, and enjoys an O(log T/T ) convergence rate for strongly convex optimization. In this paper, we make further contributions along th...

Colorization is a colour manipulation mechanism employing user-assisted colour hints for changing greyscale images into coloured ones. Several colorization algorithms have been constructed, and many of these methods are able to produce appropriately colorized images given a surprisingly sparse set of hints supplied by the user. But these colour images may not in fact look realistic. Moreover, t...

Domain adaptation is a viable solution for deep learning with small data. However, domain models trained on data sensitive information may be violation of personal privacy. In this article, we proposed unsupervised adaptation, called DP-CUDA, which based differentially private gradient projection and contradistinguisher. Compared the traditional process, DP-CUDA involves searching domain-invari...

Combining the techniques of the working set identification and generalized gradient projection, we present a new generalized gradient projection algorithm for minimax optimization problems with inequality constraints. In this paper, we propose a new optimal identification function, from which we provide a new working set. At each iteration, the improved search direction is generated by only one...

The paper considers a parametric optimization problem for the bar structures formulated as nonlinear programming task, where purpose function and non-linear constraints of mathematical model are continuously differentiable functions design variables. method objective gradient projection onto active surface with simultaneous correction violations has been used to solve problem. A discretization ...