This paper applies an idea of adaptive momentum for the nonlinear conjugate gradient to accelerate optimization problems in sparse recovery. Specifically, we consider two types minimization problems: a (single) differentiable function and sum non-smooth function. In first case, adopt fixed step size avoid traditional line search establish convergence analysis proposed algorithm quadratic proble...

In this paper, we proposed a new hybrid conjugate gradient algorithm for solving unconstrained optimization problems as convex combination of the Dai-Yuan algorithm, conjugate-descent and Hestenes-Stiefel algorithm. This is globally convergent satisfies sufficient descent condition by using strong Wolfe conditions. The numerical results show that nonlinear efficient robust.

In this paper, we present a new approach for solving absolute value equation (AVE) whichuse Levenberg-Marquardt method with conjugate subgradient structure. In conjugate subgradientmethods the new direction obtain by combining steepest descent direction and the previous di-rection which may not lead to good numerical results. Therefore, we replace the steepest descentdir...

In this paper, we propose a three-parameter family of conjugate gradient methods for unconstrained optimization. The three-parameter family of methods not only includes the already existing six practical nonlinear conjugate gradient methods, but subsumes some other families of nonlinear conjugate gradient methods as its subfamilies. With Powell’s restart criterion, the three-parameter family of...

Following the setting of the Dai-Liao (DL) parameter in conjugate gradient (CG) methods‎, ‎we introduce two new parameters based on the modified secant equation proposed by Li et al‎. ‎(Comput‎. ‎Optim‎. ‎Appl‎. ‎202:523-539‎, ‎2007) with two approaches‎, ‎which use an extended new conjugacy condition‎. ‎The first is based on a modified descent three-term search direction‎, ‎as the descent Hest...

In this paper, by linearly combining the numerator and denominator terms of Dai-Liao (DL) Bamigbola-Ali-Nwaeze (BAN) conjugate gradient methods (CGMs), a general form DL-BAN method has been proposed. From form, new hybrid CGM, which was found to possess sufficient descent property is generated. Numerical experiment carried out on CGM in comparison with four existing CGMs, using some set large s...

New accelerated nonlinear conjugate gradient algorithms which are mainly modifications of the Dai and Yuan’s for unconstrained optimization are proposed. Using the exact line search, the algorithm reduces to the Dai and Yuan conjugate gradient computational scheme. For inexact line search the algorithm satisfies the sufficient descent condition. Since the step lengths in conjugate gradient algo...