  This Letter describes a search for Higgs boson pair production using the
combined results from four final states: bb$\gamma\gamma$, bb$\tau\tau$, bbbb,
and bbVV, where V represents a W or Z boson. The search is performed using data
collected in 2016 by the CMS experiment from LHC proton-proton collisions at
$\sqrt{s} =$ 13 TeV, corresponding to an integrated luminosity of 35.9
fb$^{-1}$. Limits are set on the Higgs boson pair production cross section. A
95% confidence level observed (expected) upper limit on the nonresonant
production cross section is set at 22.2 (12.8) times the standard model value.
A search for narrow resonances decaying to Higgs boson pairs is also performed
in the mass range 250-3000 GeV. No evidence for a signal is observed, and upper
limits are set on the resonance production cross section.
