A dai-liao hybrid hestenes-stiefel and fletcher-revees methods for unconstrained optimization

Some problems have no analytical solution or too difficult to solve by scientists, engineers, and mathematicians, so the development of numerical methods to obtain approximate solutions became necessary. Gradient methods are more efficient when the function to be minimized continuously in its first derivative. Therefore, this article presents a new hybrid Conjugate Gradient (CG) method to solve unconstrained optimization problems. The method requires the first-order derivatives but overcomes the steepest descent method’s shortcoming of slow convergence and needs not to save or compute the second-order derivatives needed by the Newton method. The CG update parameter is suggested from the Dai-Liao conjugacy condition as a convex combination of Hestenes-Stiefel and Fletcher-Revees algorithms by employing an optimal modulating choice parameterto avoid matrix storage. Numerical computation adopts an inexact line search to obtain the step-size that generates a decent property, showing that the algorithm is robust and efficient. The scheme converges globally under Wolfe line search, and it’s like is suitable in compressive sensing problems and M-tensor systems

A dai-liao hybrid conjugate gradient method for unconstrained optimization

One of todays’ best-performing CG methods is Dai-Liao (DL) method which depends on non-negative parameter  and conjugacy conditions for its computation. Although numerous optimal selections for the parameter were suggested, the best choice of  remains a subject of consideration. The pure conjugacy condition adopts an exact line search for numerical experiments and convergence analysis. Though, a practical mathematical experiment implies using an inexact line search to find the step size. To avoid such drawbacks, Dai and Liao substituted the earlier conjugacy condition with an extended conjugacy condition. Therefore, this paper suggests a new hybrid CG that combines the strength of Liu and Storey and Conjugate Descent CG methods by retaining a choice of Dai-Liao parameterthat is optimal. The theoretical analysis indicated that the search direction of the new CG scheme is descent and satisfies sufficient descent condition when the iterates jam under strong Wolfe line search. The algorithm is shown to converge globally using standard assumptions. The numerical experimentation of the scheme demonstrated that the proposed method is robust and promising than some known methods applying the performance profile Dolan and Mor´e on 250 unrestricted problems.  Numerical assessment of the tested CG algorithms with sparse signal reconstruction and image restoration in compressive sensing problems, file restoration, image video coding and other applications. The result shows that these CG schemes are comparable and can be applied in different fields such as temperature, fire, seismic sensors, and humidity detectors in forests, using wireless sensor network techniques

Plasma Dynamics

Contains table of contents for Section 2 and reports on three research projects.U.S. Navy - Office of Naval Research Grant N00014-90-J-4130Princeton University/Tokamak Physics Experiment Grant S-03688-GU.S. Department of Energy Grant DE-FG02-91-ER-54109National Science Foundation Grant ATM 94-2428

Evaluation of peste des petits ruminant and Rinderpest virus infection of camels in Borno and Kano states of Nigeria

No Abstract.Nigerian Veterinary Journal Vol. 29 (3) 2008: pp. 76-7

Plasma Dynamics

Contains table of contents for Section 2 and reports on three research projects.U.S. Air Force - Office of Scientific Research Grant F49620-93-1-0108U.S. Army - Harry Diamond Laboratories Contract DAAL02-89-K-0084U.S. Army - Harry Diamond Laboratories Contract DAAL02-92-K-0037U.S. Department of Energy Grant DE-FG02-91ER-40648U.S. Navy - Office of Naval Research Grant N00014-90-J-4130National Science Foundation Contract ECS 94-42438U.S. Department of Energy Grant DE-FG02-91-ER-54109Magnetic Fusion Science Fellowship Progra