Two Improved Conjugate Gradient Methods with Application in Compressive Sensing and Motion Control

Application of frames in Chebyshev and conjugate gradient methods

‎Given a frame of a separable Hilbert space $H$‎, ‎we present some‎ ‎iterative methods for solving an operator equation $Lu=f$‎, ‎where $L$ is a bounded‎, ‎invertible and symmetric‎ ‎operator on $H$‎. ‎We present some algorithms‎ ‎based on the knowledge of frame bounds‎, ‎Chebyshev method and conjugate gradient method‎, ‎in order to give some‎ ‎approximated solutions to the problem‎. ‎Then we i...

Extensions of the Hestenes-Stiefel and Polak-Ribiere-Polyak conjugate gradient methods with sufficient descent property

Using search directions of a recent class of three--term conjugate gradient methods, modified versions of the Hestenes-Stiefel and Polak-Ribiere-Polyak methods are proposed which satisfy the sufficient descent condition. The methods are shown to be globally convergent when the line search fulfills the (strong) Wolfe conditions. Numerical experiments are done on a set of CUTEr unconstrained opti...

Multilevel Conjugate Gradient Methods

Remote Sensing Methods by Compressive Sensing

Compressive Sensing is a recently developed technique that exploits the sparsity of naturally occurring signals and images to solve inverse problems when the number of samples is less than the size of the original signal. We apply this technique to solve underdetermined inverse problems that commonly occur in remote sensing, including superresolution, image fusion and deconvolution. We use l 1-...

Two new conjugate gradient methods based on modified secant equations

Following the approach proposed by Dai and Liao, we introduce two nonlinear conjugate gradient methods for unconstrained optimization problems. One of our proposedmethods is based on a modified version of the secant equation proposed by Zhang, Deng and Chen, and Zhang and Xu, and the other is based on the modified BFGS update proposed by Yuan. An interesting feature of our methods is their acco...