We study the origin of large abundances of complex organic molecules in the Galactic center (GC). We carried out a systematic study of the complex organic molecules CH3OH, C2H5OH, (CH3)2O, HCOOCH3, HCOOH, CH3COOH, H2CO, and CS toward 40 GC molecular clouds. Using the LTE approximation, we derived the physical properties of GC molecular clouds and the abundances of the complex molecules.The CH3OH abundance between clouds varies by nearly two orders of magnitude from 2.4x10^{-8} to 1.1x10^{-6}. The abundance of the other complex organic molecules relative to that of CH3OH is basically independent of the CH3OH abundance, with variations of only a factor 4-8. The abundances of complex organic molecules in the GC are compared with those measured in hot cores and hot corinos, in which these complex molecules are also abundant. We find that both the abundance and the abundance ratios of the complex molecules relative to CH3OH in hot cores are similar to those found in the GC clouds. However, hot corinos show different abundance ratios than observed in hot cores and in GC clouds. The rather constant abundance of all the complex molecules relative to CH3OH suggests that all complex molecules are ejected from grain mantles by shocks. Frequent (similar 10^{5}years) shocks with velocities >6km/s are required to explain the high abundances in gas phase of complex organic molecules in the GC molecular clouds. The rather uniform abundance ratios in the GC clouds and in Galactic hot cores indicate a similar average composition of grain mantles in both kinds of regions. The Sickle and the Thermal Radio Arches, affected by UV radiation, show different relative abundances in the complex organic molecules due to the differentially photodissociation of these molecules.