A priori estimates on the length of the primal-dual path that results from a MoreauYosida approximation of the feasible set for state constrained optimal control problems are derived. These bounds depend on the regularity of the state and the dimension of the problem. Numerical results indicate that the bounds are indeed sharp and are typically attained in cases where the active set consists of...

The simplex solution algorithm for linear programs (LP) can be considered as a sub-gradient direction method therefore a full gradient solution algorithm might be more efficient. We have developed a full gradient method which consists of three phases. The initialization phase provides the initial tableau which may not have a full set of basis. The push phase uses a full gradient vector of the o...

The discrete Fourier transform (DFT) algorithms are commonly used in frequency estimation. The interpolation direction of the interpolated algorithms based on DFT is always defined by the information of spectral amplitude, such as the Rife algorithm. In the case of low signal to noise ratio (SNR), false decision of the interpolation direction occurs sometimes. However, decreasing false rate of ...

With the development of compressive sensing theory, image reconstruction from few-view projections has received considerable research attentions in the field of computed tomography (CT). Total-variation- (TV-) based CT image reconstruction has been shown to be experimentally capable of producing accurate reconstructions from sparse-view data. In this study, a distributed reconstruction algorith...

Recently, communication between participants about children’s development has become more necessary in kindergartens and nurseries. Thus, we have been developing an Interactive Communication System through which participants communicate about childhood education using motion pictures recorded in kindergartens and nurseries. This system requires ex-post selection of motion pictures. However, sin...

The Alternating Direction Method of Multipliers (ADMM) has received lots of attention recently due to the tremendous demand from large-scale and data-distributed machine learning applications. In this paper, we present a stochastic setting for optimization problems with non-smooth composite objective functions. To solve this problem, we propose a stochastic ADMM algorithm. Our algorithm applies...

This paper proposes efficient algorithms for group sparse optimization with mixed `2,1-regularization, which arises from the reconstruction of group sparse signals in compressive sensing, and the group Lasso problem in statistics and machine learning. It is known that encoding the group information in addition to sparsity will lead to better signal recovery/feature selection. The `2,1-regulariz...

In this paper, we propose an efficient alternating direction implicit (ADI) Galerkin method for solving the time-fractional partial differential equation with damping, where the fractional derivative is in the sense of Caputo with order in (1, 2). The presented numerical scheme is based on the L2-1σ method in time and the Galerkin finite element method in space. The unconditional stability and ...

Online optimization has emerged as powerful tool in large scale optimization. In this paper, we introduce efficient online optimization algorithms based on the alternating direction method (ADM), which can solve online convex optimization under linear constraints where the objective could be nonsmooth. We introduce new proof techniques for ADM in the batch setting, which yields a O(1/T ) conver...

In this paper we present a new line search method known as the HBFGS method, which uses the search direction of the conjugate gradient method with the quasi-Newton updates. The Broyden-Fletcher-Goldfarb-Shanno (BFGS) update is used as approximation of the Hessian for the methods. The new algorithm is compared with the BFGS method in terms of iteration counts and CPU-time. Our numerical analysis...