A major difficulty in applying computational design methods to nanophotonic devices is ensuring that the resulting designs are fabricable. Here, we describe a general inverse design algorithm for nanophotonic devices that directly incorporates fabrication constraints. To demonstrate the capabilities of our method, we designed a spatial-mode demultiplexer, wavelength demultiplexer, and directional coupler. We also designed and experimentally demonstrated a compact, broadband 1 × 3 power splitter on a silicon photonics platform. The splitter has a footprint of only 3.8 × 2.5 μm, and is well within the design rules of a typical silicon photonics process, with a minimum radius of curvature of 100 nm. Averaged over the designed wavelength range of 1400-1700 nm, our splitter has a measured insertion loss of 0.642 ± 0.057 dB and power uniformity of 0.641 ± 0.054 dB.