Efficient newton-raphson/singular value decomposition-based optimization scheme with dynamically updated critical...

Area of Science:

• Computational Chemistry
• Numerical Optimization

Background:

• Optimization is crucial for practical problems, but challenging for multidimensional functions with statistical data.
• Existing methods like direct iteration and conventional Newton-Raphson (NR) may not be sufficiently robust or efficient.

Purpose of the Study:

• To propose and demonstrate a novel, robust optimization scheme for complex computational problems.
• To enhance the efficiency and accuracy of solving multidimensional optimization tasks.

Main Methods:

• Developed the NR/SVD-Cdyn scheme, integrating the Newton-Raphson (NR) method with singular value decomposition (SVD).
• Applied the NR/SVD-Cdyn scheme to solve a system of weighted histogram analysis method equations.

Main Results:

• The NR/SVD-Cdyn scheme demonstrated significant performance improvements compared to direct iteration and conventional NR methods.
• Numerical solutions obtained using the proposed scheme were robust and accurate.

Conclusions:

• The NR/SVD-Cdyn scheme offers a universal and effective approach for complex optimization problems.
• This method has broad applicability in computational chemistry, including parameter fitting for molecular mechanics and quantum mechanics methods.