  We apply the model of minimally nonlinear irreversible heat engines developed
by Izumida and Okuda [EPL {\bf 97}, 10004 (2012)] to refrigerators. The model
assumes extended Onsager relations including a new nonlinear term accounting
for dissipation effects. The bounds for the optimized regime under an
appropriate figure of merit and the tight-coupling condition are analyzed and
successfully compared with those obtained previously for low-dissipation Carnot
refrigerators in the finite-time thermodynamics framework. Besides, we study
the bounds for the nontight-coupling case numerically. We also introduce a
leaky low-dissipation Carnot refrigerator and show that it serves as an example
of the minimally nonlinear irreversible refrigerator, by calculating its
Onsager coefficients explicitly.
