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Participants' performances were graded dichotomously and the strategies that students used to solve problem correctly were determined.
Moreover, the convergence of the proposed Algorithm 3 (see numerical example, Section 5) to the centralized solution shows that bracketing method can be used to solve problem (44).
The Dai-Kou type methods are very efficient in solving the unconstrained minimization, so we hope they can be used to solve problem (1) only requiring gradient information.
Based on the above analysis, the detailed steps that are used to solve problem (28) are summarized as Algorithm 3, where ρ denotes the objective function value of problem (29).
In Section 3, a modified kernel method is used to solve problem (1), and we also obtain the convergence estimates between the regularization solution and the exact solution based on the a priori assumptions for the exact solution.
The nanoparticles can also be used to solve problem of fines migration in the oil industry (Ogolo et al. 2017; Yue et al. 2018) and as drilling fluids additives to improve the rheological properties (Smith et al. 2018; Afolabi et al. 2018).
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