  We introduce the iterative power algorithm (IPA) for global optimization and
a formal proof of convergence for both discrete and continuous global search
problems. IPA implements the power iteration method in quantics tensor train
(QTT) representations. Analogous to the imaginary time propagation method with
infinite mass, IPA starts with an initial probability distribution $\rho_0({\bf
r})$ and iteratively applies the recurrence relation $\rho_{k+1}({\bf r}) = U
\rho_k({\bf r})/ \| U \rho_k({\bf r}) \|_{L^1}$, where $U=e^{-V({\bf r})}$ is
defined in terms of the `potential energy' function $V({\bf r})$ with global
minimum at ${\bf r}={\bf r}^*$. Upon convergence, the probability distribution
becomes a delta function $\delta({\bf r}-{\bf r}^*)$, so the global minimum can
be obtained as the position expectation value ${\bf r}^* = \text{Tr}\left[{\bf
r} \delta({\bf r}-{\bf r}^*)\right]$. QTT representations of $V({\bf r})$ and
$\rho({\bf r})$ are generated by fast adaptive interpolation of
multidimensional arrays to bypass the curse of dimensionality and the need to
evaluate $V({\bf r})$ for all possible values of ${\bf r}$. We illustrate the
capabilities of IPA as applied to solving the factorization problem formulated
as a global search optimization on the "potential energy" surface $V({\bf
r})=\text{mod}(N,{\bf r})$, where $N$ is the number to be factorized and ${\bf
r}\in \{2,3,5,7,11,\dots\}$ is the space of prime numbers folded as a
$d$-dimensional $2_1 \times 2_2 \times \cdots \times 2_d$ tensor. We find that
IPA resolves multiple degenerate global minima corresponding to prime factors
of $N$ even when separated by large energy barriers in the highly rugged
landscape of $V({\bf r})$. Therefore, IPA should be of great interest for a
wide range of other optimization problems ubiquitous in molecular and
electronic structure calculations.
