  We perform a multivariate analysis of Higgs-pair production via the decay
channel $HH \to b\bar b \gamma\gamma$ at the future 100 TeV $pp$ collider to
determine the trilinear Higgs self--coupling (THSC) $\lambda_{3H}$, which takes
the value of 1 in the standard model. We consider all known background
processes. For the signal we adopt the most recent event generator of {\tt
POWHEG-BOX-V2} to exploit the NLO distributions for Toolkit for Multivariate
Data Analysis (TMVA). Through the technique of Boosted Decision Tree (BDT)
analysis trained for $\lambda_{3H}=1$, compared to the the conventional
cut-and-count approach, the signal-to-background ratio improves tremendously
from about $1/10$ to $1$ and the significance can reach up to $20.5$ with a
luminosity of 3 ab$^{-1}$ without including systematic uncertainties. In
addition, by implementing a likelihood fitting of the signal-plus-background
$M_{\gamma\gamma b b}$ distribution with optimized bin sizes, it is possible to
determine the THSC with the precision of 7.5\% at 68\% CL even at the early
stage of 100 TeV hadron collider with 3 ab$^{-1}$.
