In this paper, we investigate a spectral Petrov-Galerkin method for an optimal control problem governed by two-sided space-fractional diffusion-advection-reaction equation. Taking into account the effect of singularities near boundary generated weak singular kernel fractional operator, establish regularity in weighted Sobolev space. Error estimates are provided presented and convergence orders ...

The aim of this paper is to study the convergence properties of the gradient projection method and to apply these results to algorithms for linearly constrained problems. The main convergence result is obtained by defining a projected gradient, and proving that the gradient projection method forces the sequence of projected gradients to zero. A consequence of this result is that if the gradient...

In this paper we propose a subspace limited memory quasi-Newton method for solving large-scale optimization with simple bounds on the variables. The limited memory quasi-Newton method is used to update the variables with indices outside of the active set, while the projected gradient method is used to update the active variables. The search direction consists of three parts: a subspace quasi-Ne...

This paper considers reconstructing a spectrally sparse signal from a small number of randomly observed time-domain samples. The signal of interest is a linear combination of complex sinusoids at R distinct frequencies. The frequencies can assume any continuous values in the normalized frequency domain [0, 1). After converting the spectrally sparse signal recovery into a low rank structured mat...

A family of variable metric methods for convex constrained optimization was introduced recently by Birgin, Mart́ınez and Raydan. One of the members of this family is the Inexact Spectral Projected Gradient (ISPG) method for minimization with convex constraints. At each iteration of these methods a strictly convex quadratic function with convex constraints must be (inexactly) minimized. In the ca...

In this paper, we propose a method to solve the distributed optimal power flow problem and discuss the associated implementation. We have combined this method with a projected Jacobi (PJ) method and a modified parallel block scaled gradient (MPBSG) method possessing decomposition effects. With the decomposition, our method can be parallel processed and is computationally efficient. We have test...

Tensor regression has shown to be advantageous in learning tasks with multi-directional relatedness. Given massive multiway data, traditional methods are often too slow to operate on or suffer from memory bottleneck. In this paper, we introduce subsampled tensor projected gradient to solve the problem. Our algorithm is impressively simple and efficient. It is built upon projected gradient metho...

In this paper we propose a subspace limited memory quasi-Newton method for solving large-scale optimization with simple bounds on the variables. The limited memory quasi-Newton method is used to update the variables with indices outside of the active set, while the projected gradient method is used to update the active variables. The search direction consists of three parts: a subspace quasi-Ne...

The problem of best approximating a given real matrix in the Frobenius norm by real normal matrices subject to a prescribed spectrum is consid ered The approach is based on using the projected gradient method The projected gradient of the objective function on the manifold of constraints can be formulated explicitly This gives rise to a descent ow that can be followed numerically The explicit f...

We present a new approach to solving nonlinear complementarity problems based on the normal map and adaptations of the projected gradient algorithm. We characterize a Gauss{Newton point for nonlinear complementarity problems and show that it is suucient to check at most two cells of the related normal manifold to determine such points. Our algorithm uses the projected gradient method on one cel...