  A search for anomalous electroweak production of WW, WZ, and ZZ boson pairs
in association with two jets in proton-proton collisions at $\sqrt{s} =$ 13 TeV
at the LHC is reported. The data sample corresponds to an integrated luminosity
of 35.9 fb$^{-1}$ collected with the CMS detector. Events are selected by
requiring two jets with large rapidity separation and invariant mass, one or
two leptons (electrons or muons), and a W or Z boson decaying hadronically. No
excess of events with respect to the standard model background predictions is
observed and constraints on the structure of quartic vector boson interactions
in the framework of dimension-8 effective field theory operators are reported.
Stringent limits on parameters of the effective field theory operators are
obtained. The observed 95% confidence level limits for the S0, M0, and T0
operators are $-$2.7 $<$ f$_{\mathrm{S0}}/ \Lambda^{4}$ $<$ 2.7, $-$1.0 $<$
f$_{\mathrm{M0}}/ \Lambda^{4}$ $<$ 1.0, and $-$0.17 $<$ f$_{\mathrm{T0}}/
\Lambda^{4}$ $<$ 0.16, in units of TeV$^{-4}$. Constraints are also reported on
the product of the cross section and branching fraction for vector boson fusion
production of charged Higgs bosons as a function of mass from 600 to 2000 GeV.
The results are interpreted in the context of the Georgi-Machacek model.
