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2 changes: 1 addition & 1 deletion docs/advanced/input_files/input-main.md
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Expand Up @@ -1369,7 +1369,7 @@ These variables are used to control the geometry relaxation.
- **Description**: The methods to do geometry optimization.
- cg: using the conjugate gradient (CG) algorithm. Note that there are two implementations of the conjugate gradient (CG) method, see [relax_new](#relax_new).
- bfgs: using the Broyden–Fletcher–Goldfarb–Shanno (BFGS) algorithm.
- bfgs_trad: using BFGS algorithm consistent with the BFGS algorithm in ASE.
- bfgs_trad: using the standard Broyden–Fletcher–Goldfarb–Shanno (BFGS) algorithm.
- cg_bfgs: using the CG method for the initial steps, and switching to BFGS method when the force convergence is smaller than [relax_cg_thr](#relax_cg_thr).
- sd: using the steepest descent (SD) algorithm.
- fire: the Fast Inertial Relaxation Engine method (FIRE), a kind of molecular-dynamics-based relaxation algorithm, is implemented in the molecular dynamics (MD) module. The algorithm can be used by setting [calculation](#calculation) to `md` and [md_type](#md_type) to `fire`. Also ionic velocities should be set in this case. See [fire](../md.md#fire) for more details.
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4 changes: 2 additions & 2 deletions docs/advanced/opt.md
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Expand Up @@ -24,9 +24,9 @@ The [BFGS method](https://en.wikipedia.org/wiki/Broyden%E2%80%93Fletcher%E2%80%9

In ABACUS, we implemented the BFGS method for doing fixed-cell structural relaxation.

### BFGS_TRAD method
We have alse implemented an alternative BFGS method, which can be called by using the keyword 'bfgs_trad'.

The BFGS_TRAD method is an algorithm implemented in ABACUS, referencing the BFGS method from ASE. The previous BFGS method in ABACUS did not perform well for some tests and the BFGS_TRAD method now produces results that are consistant with the BFGS method in ASE. In cases where the previous BFGS method could not converge within a limited number of steps, the BFGS_TRAD method can successfully converge.
The bfgs_trad method is a quasi-Newton method that substitute an approximate matrix B for the Hessian matrix. The optimization direction is determined by the inverse of B, therefore, only the inverse of B is iteratively updated and no time-consuming operations such as matrix inversion are involved.

### SD method

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