Abstract
In this work, motivated by the effect of inertial step in accelerating algorithms for solving nonlinear problems such as equilibrium problems, we propose two hybrid spectral algorithms with inertial effect for solving system of nonlinear equations with convex constraints. The search directions in these algorithms use the convex combination of the modified Barzilai and Borwein spectral parameters (IMA journal of numerical analysis, vol. 8, no. 1, pp. 141-148, 1988) and their geometric mean proposed by Dai et al. (In Numerical Analysis and Optimization, pp. 59-75, Springer, 2015). The incorporation of the inertial-step aids the proposed algorithms in producing more efficient results in comparison with three existing spectral algorithms. Under the assumption that the function under consideration is monotone and satisfies Lipschitz continuity, we prove the global convergence of the proposed algorithms. In addition, we also show the application of the proposed algorithms in motion control of two-joint planar robotic manipulator.
Highlights
In this work, motivated by the effect of inertial step in accelerating algorithms for solving nonlinear problems such as equilibrium problems, we propose two hybrid spectral algorithms with inertial effect for solving system of nonlinear equations with convex constraints
Many problems appearing in engineering, physical and social sciences can be transformed into system of nonlinear equations and equilibrium problems
We propose two new hybrid spectral algorithms for solving system of nonlinear equations based on the inertial effect
Summary
Many problems appearing in engineering, physical and social sciences can be transformed into system of nonlinear equations and equilibrium problems. La Cruz et al [19] proposed another derivative free spectral residual method for solving large scale system of nonlinear equations They proved the global convergence of the method and presented some numerical experiments. The search direction in their algorithm is based on the convex combination of the modified Barzilai and Borwein (BB) spectral gradient parameter [24] and a positive spectral coefficient of Dai et al [25] In [30], Vinh and Muu proposed an inertial iterative algorithm for solving pseudomonotone equilibrium problems in real Hilbert space They introduced the inertial effect in order to accelerate the speed of the iteration process.
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