Conjugate gradient minimization

The advantage of a conjugate gradient minimizer is that it uses the minimization history to calculate the search direction, and converges faster than the steepest descent technique. It also contains a scaling factor, b, for determining step size. This makes the step sizes optimal when compared to the steepest descent technique. 

Example Compare the steps of a conjugate gradient minimization with the steepest descent method. Amolecular system can reach a potential minimum after the second step if the first step proceeds from A to B. If the first step is too large, placing the system at D, the second step still places the system near the minimum(E) because the optimizer remembers the penultimate step. 

The set of Kohn-Sham-like linear equations above represents the working equations of DFPT. They are usually solved by iterative linear algebra algorithms (conjugate-gradient minimization). 

The CPR method is the most difficult method to implement, beeause of the complex rules for adding or rejecting points on the path. It is also the least efficient of the methods tested. It does, however, converge quickly to the saddle point once it is close, as is evident from comparing table 1 and 2. This is probably because of the use of the conjugate gradient minimization which is quite efficient. 

Fried, I., "N-Step Conjugate Gradient Minimization Scheme... 

Stich, R. Car, M. Parrinello, and S. Baroni, Conjugate gradient minimization of the energy functional A new method for electronic structure calculation, Phys. Rev. B Condens. Matter, 39 (1989), 4997-5004. 

Side chain conformations were minimized by 600 cycles of conjugate gradient minimization (Powell method) and saved. We observed that 600 cycles of minimization allows convergence in a reasonable time. 

Starting from the conformations in (1), we applied 600 cycles of conjugate gradient minimization to all atoms of the loop. 

Figure 3. The segment consisting of residues Cys-192 and His-193 of the 2.8 A resolution structure of a single site mutant of aspartate aminotransferase [23]. Superimposed are the initial structure (dotted lines) obtained by fitting the atomic model to a multiple isomorphous replacement map, the structure obtained after several cycles of rebuilding and restrained least-squares refinement (thick lines), the structure obtained after simulated annealing refinement (thin lines), and the structure obtained after conjugate gradient minimization (dashed lines).

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