Two Hybrid Spectral Methods With Inertial Effect for Solving System of Nonlinear Monotone Equations With Application in Robotics

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.