A linear surrogate for optimising functions of an orthogonal matrix with applications in wave function theory
Abstract
The technique of surrogate optimisation is to use a simpler function to approximate a complex function that is time-consuming to evaluate. We show that the maximum of a special type of surrogate function (Formula presented.) is at (Formula presented.), and that there is one and only one local maximum both in (Formula presented.) and (Formula presented.). This function (Formula presented.) has been found to be useful in various aspects of electronic structure theory, including proving the Carlson-Keller theorem, and localising orbitals. As one other example, we apply it here to optimise the ground state of molecules using the Generalised Valence Bond wavefunction.
Many UC-authored scholarly publications are freely available on this site because of the UC's open access policies. Let us know how this access is important for you.