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In this paper, we consider a variational inequality problem which is defined over the intersection of the set of common fixed points of a finite family of generalized demimetric mappings and the set of common zero points of a finite family of maximal monotone mappings. We propose an iterative algorithm which combines the hybrid steepest descent method with the inertial technique to solve this variational inequality problem. Strong convergence theorem of the proposed method is established under standard and mild conditions. Moreover, we do not require any prior information regarding the Lipschitz and strongly monotone constants of the mapping. The results of this paper improve and extend several known results in the literature. [ABSTRACT FROM AUTHOR]

We propose a new and efficient nonmonotone adaptive trust region algorithm to solve unconstrained optimization problems. This algorithm incorporates two novelties: it benefits from a radius dependent shrinkage parameter for adjusting the trust region radius that avoids undesirable directions and exploits a new strategy to prevent sudden increments of objective function values in nonmonotone trust region techniques. Global convergence of this algorithm is investigated under some mild conditions. Numerical experiments demonstrate the efficiency and robustness of the proposed algorithm in solving a collection of unconstrained optimization problems from the CUTEst package. [ABSTRACT FROM AUTHOR]

In this paper, we consider a variational inequality problem which is defined over the intersection of the solution set of variational inequality problem and the solution set of split common fixed point problem for averaged operators in Hilbert spaces. We present a new and efficient iterative method for solving this problem and establish its strong convergence. The proposed algorithm does not require knowledge of the Lipschitz constants of the operators and does not depend on the prior information of the bounded linear operator norms. Finally, we apply our result to study certain classes of optimization problems, and present some numerical experiments to demonstrate the applicability of our proposed algorithm. [ABSTRACT FROM AUTHOR]

Multipoint secant and interpolation methods are effective tools for solving systems of nonlinear equations. They use quasi-Newton updates for approximating the Jacobian matrix. Owing to their ability to more completely utilize the information about the Jacobian matrix gathered at the previous iterations, these methods are especially efficient in the case of expensive functions. They are known to be local and superlinearly convergent. We combine these methods with the nonmonotone line search proposed by Li and Fukushima (2000), and study global and superlinear convergence of this combination. Results of numerical experiments are presented. They indicate that the multipoint secant and interpolation methods tend to be more robust and efficient than Broyden’s method globalized in the same way. [ABSTRACT FROM AUTHOR]

Projection based methods are a family of efficient and applicable derivative free methods for solving systems of nonlinear monotone equations. These methods, at each iteration, use a backtracking line search to generate a hyperplane which strictly separates the current approximation from the solution set of the problem. Numerical experiments indicate that choosing an appropriate line search highly affects the efficiency of projection based methods. In this paper we introduce a new line search procedure for generating the separating hyperplane. The convergence properties of the new procedure is established in a simple and short way. Numerical results show that the new line search is very effective and increases the efficiency of projection based methods. [ABSTRACT FROM AUTHOR]

In this paper, we propose a derivative free algorithm for solving large-scale nonlinear systems of monotone equations which combines a new idea of projection methodology with a line search strategy, while an improvement in the projection step is exerted. At each iteration, the algorithm constructs two appropriate hyperplanes which strictly separate the current approximation from the solution set of the problem. Then the new approximation is determined by projecting the current point onto the intersection of two halfspaces that are constructed by these hyperplanes and contain the solution set of the problem. Under some mild conditions, the global convergence of the algorithm is established. Preliminary numerical results indicate that the proposed algorithm is promising. [ABSTRACT FROM AUTHOR]

In this paper, we propose a hybrid conjugate gradient method for unconstrained optimization, obtained by a convex combination of the LS and KMD conjugate gradient parameters. A favourite property of the proposed method is that the search direction satisfies the Dai–Liao conjugacy condition and the quasi-Newton direction. In addition, this property does not depend on the line search. Under a modified strong Wolfe line search, we establish the global convergence of the method. Numerical comparison using a set of 109 unconstrained optimization test problems from the CUTEst library show that the proposed method outperforms the Liu–Storey and Hager–Zhang conjugate gradient methods. [ABSTRACT FROM AUTHOR]

In this paper, a hybrid derivative-free conjugate gradient method that inherits the structures of two conjugate gradient methods is introduced to recover sparse signal in compressive sensing by solving the nonlinear convex constrained equations. The global convergence of the proposed method is proved, under some appropriate assumptions. Numerical experiments and comparisons suggest that the proposed algorithm is an efficient approach for sparse signal and image reconstruction in compressive sensing. [ABSTRACT FROM AUTHOR]

The present study aims to investigate exergy efficiency of a Flat-plate solar collector containing Al 2 O 3 –water nanofluid as base fluid. The effect of various parameters like mass flow rate of fluid, nanoparticle volume concentration, collector inlet fluid temperature, solar radiation, and ambient temperature on the collector exergy efficiency is investigated. Also, the procedure to determine optimum values of nanoparticle volume concentration, mass flow rate of fluid, and collector inlet fluid temperature for maximum exergy efficiency delivery has been developed by means of interior-point method for constrained optimization under the given conditions. According to the results, each of these parameters can differently affect the collector exergy by changing the value of the other parameters. The optimization results indicate that under the actual constraints, in both pure water and nanofluid cases the optimized exergy efficiency is increased with increasing solar radiation value. By suspending Al 2 O 3 nanoparticles in the base fluid (water) the maximum collector exergy efficiency is increased about 1% and also the corresponding optimum values of mass flow rate of fluid and collector inlet fluid temperature are decreased about 68% and 2%, respectively. [ABSTRACT FROM AUTHOR]