**An energy minimization strategy based on an improved nonlinear conjugate
gradient method for accelerating the charged polymer dynamics simulation**

H Lin and YW Shi and EL Shang and SY Dai, PHYSICAL CHEMISTRY CHEMICAL PHYSICS, 25, 12290-12307 (2023).

DOI: 10.1039/d2cp05839a

Using a hybrid simulation method that combines a non-linear conjugate gradient (NCG) method for solving large-scale unconstrained optimization problems with a Brownian dynamics (BD) model for polymer chains, we investigate the pre-equilibrium simulation of charged polymers in different dielectric systems from an energy minimization perspective. We propose an improved NCG coefficient (beta(LPRP)(k)) that satisfies a sufficient descent condition with a greater parameter sigma is an element of(0, 1/2) under a strong Wolfe line search and converges globally for nonconvex minimization. Furthermore, preliminary numerical results show that the beta(LPRP)(k) coefficient is more efficient than many existing NCG coefficients for a large number of practical test problems from our model. We further compare the performance of the improved NCG method with that of other mainstream numerical methods in energy minimization, and the simulation results suggest that the NCG method is more competitive in terms of cost-effectiveness. Importantly, we apply the geometrically optimized configuration obtained by performing the NCG method to the pre-equilibrium simulation, and the numerical results show that it increases the computational efficiency of a pure solvent and biomolecule-solution systems at most by about 32 and 70 times, respectively, with the relative energy errors being controlled below 1 x 10(-2) and 4.5 x 10(-3), respectively. More importantly, the final pre-equilibrium configuration of the BD simulation that performs energy minimization and the traditional BD simulation matched closely.

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