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In this paper, we present a new hybrid spectral-conjugate gradient (SCG) algorithm for finding approximate solutions to nonlinear monotone operator equations. The hybrid conjugate gradient parameter has the Polak–Ribière–Polyak (PRP), Dai–Yuan (DY), Hestenes–Stiefel (HS) and Fletcher–Reeves (FR) as special cases. Moreover, the spectral parameter is selected such that the search direction has the descent property. Also, the search directions are bounded and the sequence of iterates generated by the new hybrid algorithm converge globally. Furthermore, numerical experiments were conducted on some benchmark nonlinear monotone operator equations to assess the efficiency of the proposed algorithm. Finally, the algorithm is shown to have the ability to recover disturbed signals. [ABSTRACT FROM AUTHOR]

In this article, we propose a hybrid conjugate gradient (CG) scheme for solving unconstrained optimization problem. The search direction is a combination of the Polak–Ribière–Polyak (PRP) and the Liu–Storey (LS) CG parameters and is close to the direction of the memoryless Broyden–Fletcher–Goldfarb–Shanno (BFGS) quasi-Newton scheme. Without the use of the line search, the search direction satisfies the descent condition and possesses the trust region property. The global convergence of the scheme for general functions under the Wolfe-type and Armijo-type line search is established. Numerical experiments are carried out on some benchmark test problems and the results show that the propose scheme is more efficient than other existing schemes. Finally, a practical application of the scheme in motion control of robot manipulator is also presented. [ABSTRACT FROM AUTHOR]

The main objective of this paper is to introduce two new proximal-like methods to solve the equilibrium problem in a real Hilbert space. The equilibrium problem is a general mathematical problem that unites several useful mathematical problems, including optimization problems, variational inequalities, fixed-point problems, saddle point problems, complementary problems, and Nash equilibrium problems. Both new methods are analogous to the well-known extragradient method, which has been used in the literature to solve variational inequality problems. The proposed methods make use of a non-monotone variable step size rule that is revised for each iteration and is determined mainly by previous iterations. The advantage of these methods is that they can be used without prior knowledge of Lipschitz-type constants or any line-search method. By allowing for some mild condition, the strong convergence of both methods is established. Numerical studies are presented to demonstrate the computational behavior of new methods and to compare them to other existing methods. • Two extragradient methods are proposedfor solving an equilibrium problem involving pseudomonotone bifunction • Strong convergence is obtained by using Mann and Viscosity type iterative schemes • Applications to solve variational inequality problems and fixed point problems are presented • A comprehensive numerical analysis is considered to show competitive advantage of proposed methods [ABSTRACT FROM AUTHOR]

In this work, a generalized unsteady magnetohydrodynamic transport of a rate type fluid near an unbounded upright plate is analyzed under Newtonian heating and non-uniform velocity conditions. The vertical plate is suspended in a porous medium and is encountering the radiation effects. Three different fractional models for Maxwell fluid are established by using the modern definitions of Atangana–Baleanu, Caputo–Fabrizio, and Caputo fractional operators. Triple fractional analysis is conducted to reach out to the solutions of consequent flow and energy equations. Laplace transform and Stehfest's numerical algorithm are jointly applied to solve each fractional model. Shear stress and heat transfer rate are measured at the solid–fluid interface in the form of skin friction coefficient and Nusselt number respectively. The physical significance of associated parameters in velocity and energy boundary layers is investigated and graphs are provided to discuss the relevant physical arguments. A tabular analysis is performed to demonstrate the influence of physical parameters on shear stress and heat transfer rate. An empirical comparison between fractional and classical solutions indicates that fractional operators provide a better explanation of the physical features of the model. It is also analyzed that for Newtonian heating and non-uniform velocity conditions, the Atangana–Baleanu fractional operator is the finest fractional model to describe the memory effect of velocity and energy distribution. The velocity of a Maxwell fluid is always higher for constant velocity condition as compared to the ramped velocity condition. Furthermore, the heat transfer rate declines for increasing values of the fractional parameter α and a minimum value is witnessed for the classical model but, it follows an inverse trend when the radiation parameter R d increases. [ABSTRACT FROM AUTHOR]

• We compared the proposed algorithm MSP with three similar existing algorithms, namely; SGCS [29], PCG [22] and CGD [30]. • Numerical experiments show that MSP outperforms PCG and CGD in signal recovery problems and it restored image with high quality than SGCS and CGD methods. • The proposed algorithm is an extension of the method for solving signal and image restoration problems. • Some nice properties of the algorithm are that it is derivative-free as well as matrix-free. We present a Barzilai-Borwein gradient method using the hyperplane projection technique of Solodov and Svaiter (1998) for solving the non-smooth nonlinear monotone equation arising from the reformulation of the ℓ 1 -norm regularized problem. The proposed method is an extension of the modified method by Liu and Duan (J. Inequal. Appl. 2015(1), 8, 2015) for solving signal and image restoration problems. The method is derivative-free and its search direction satisfies the sufficient descent condition. Numerical experiments presented show that the proposed method can recover sparse signals in fewer iterations and less CPU time and can reconstruct blurred images with higher quality compared to similar methods in the literature. [ABSTRACT FROM AUTHOR]

• A new dengue model with a new class known as asymptomatic carrier and with Caputo–Fabrizio derivative is proposed. • Mathematical results associated to the model is presented and sensitivity analysis. • Existence and uniqueness results are provided. • A new iterative scheme for the solution of fractional dengue model is presented. It is prominent that memory has a prodigious influence on the development of every process associated with human societies. More specifically, the growth of an epidemic process is directly associated with the individuals' experiences. In fact, the real epidemic process is obviously sustained by non-Markovian dynamics: heredity properties and memory effects perform a critical role in the subsequent spread of infection. These additional properties increase the accuracy and reliability of fractional order systems than the other ordinary systems. In this current study, a dengue infection model with asymptomatic carriers through Caputo–Fabrizio (CF) and Atangana–Baleanu (AB) fractional derivatives is introduced. Analytic skills are used to obtain the basic reproduction number for the proposed dengue model, denoted by R 0. We use partial rank correlation coefficient (PRCC) method to detect the effect of input parameters on the outcomes of R 0. In addition, we have proven sufficient condition for the existence and uniqueness of solution for the suggested fractional dynamics of dengue infection. To explore the intricate dynamics of dengue infection with the effect of asymptomatic carriers, we perform numerical simulations of the suggested dengue model by varying the fractional order ℓ. Fractional order model offers realistic information about the dynamics of the suggested dengue model and sharply decrease infected individuals by decreasing the fractional order parameter ℓ for the case of Caputo–Fabrizio model while a rapid decrease in the case of Atangana–Baleanu model. We show that the Atangana–Baleanu model gives good decrease for the infected compartments in case of decreasing the fractional order parameter than that of the Caputo–Fabrizio model. It is shown that the asymptomatic fraction can be greatly decreased by decreasing the parameter ℓ. Furthermore, the influence of the biting rate of mosquitoes on infected humans is investigated numerically, and it is suggested to the control policymakers that controlling the biting rate can significantly reduce the level of dengue infection. [ABSTRACT FROM AUTHOR]