Optimization Algorithms steepest descent

HyperChem supplies three types of optimizers or algorithms steepest descent, conjugate gradient (Hetcher-Reeves and Polak-Ribiere), and block diagonal (Newton-Raphson). 

Algorithm used for the minimization of mathematical functions (steepest descent, gradient, second-derivative and other methods). In molecular mechanics these are used to minimize the strain energy and thereby optimize the molecular structure (see molecular mechanics). 

The most popular optimization techniques are Newton-Raphson optimization, steepest ascent optimization, steepest descent optimization. Simplex optimization. Genetic Algorithm optimization, simulated annealing. - Variable reduction and - variable selection are also among the optimization techniques. 

The computational approach described here, based on the combination of the Kalman filter algorithm and iterative optimization by the simulated annealing method, was able to find the optimal alignment of the pure component peaks with respect to the shifted components in the overlapped spectra, and hence, to correctly estimate the contributions of each component in the mixture. The simulated annealing demonstrated superior ability over the other optimization methods, simplex and steepest descent, in yielding more reliable convergences at the expense of not much more computer time, at least for resolving ternary shifted overlapped spectra. 

The SCF wavefunctions from which the electron density is fitted was calculated by means of the GAUSSIAN-90 system of programs [18]. The program QMOLSIM [3] used in the computation of the MQSM allows optimization of the mutual orientation of the two systems studied in order to maximize their similarity by the common steepest-descent, Newton and quasi-Newton algorithms [19]. The DIIS procedure [20] has been also implemented for the steepest-descent optimizations in order to improve the performance of this method. The MQSM used in the optimization procedure are obtained from fitted densities. This speeds the process. The exact MQSM were obtained from the molecular orientation obtained in this optimization procedure. 

Equipped with such a method to estimate the gradient of the energy with respect to the parameters, we can describe a simple steepest descent algorithm that tries to optimize the parameters in a single VMC run. 

A molecular mechanics optimization allo vs partial to full atom flexibility of the protein through an energy minimization of the protein-ligand complexes and can be used for postprocessing of docked poses. In favor of that, various minimization methods ranging from a steepest descent to a genetic algorithm can be used [67]. 

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