  Context. Transient neutrino sources such as Gamma-Ray Bursts (GRBs) and
Supernovae (SNe) are hypothesized to emit bursts of high-energy neutrinos on a
time-scale of \lesssim 100 s. While GRB neutrinos would be produced in high
relativistic jets, core-collapse SNe might host soft-relativistic jets, which
become stalled in the outer layers of the progenitor star leading to an
efficient production of high-energy neutrinos. Aims. To increase the
sensitivity to these neutrinos and identify their sources, a low-threshold
optical follow-up program for neutrino multiplets detected with the IceCube
observatory has been implemented. Methods. If a neutrino multiplet, i.e. two or
more neutrinos from the same direction within 100 s, is found by IceCube a
trigger is sent to the Robotic Optical Transient Search Experiment, ROTSE. The
4 ROTSE telescopes immediately start an observation program of the
corresponding region of the sky in order to detect an optical counterpart to
the neutrino events. Results. No statistically significant excess in the rate
of neutrino multiplets has been observed and furthermore no coincidence with an
optical counterpart was found. Conclusion. The search allows, for the first
time, to set stringent limits on current models predicting a high-energy
neutrino flux from soft relativistic hadronic jets in core-collapse SNe. We
conclude that a sub-population of SNe with typical Lorentz boost factor and jet
energy of 10 and 3\times10^{51} erg, respectively, does not exceed 4.2% at 90%
confidence.
