Purpose: To develop an ultra-fast web-based inverse planning framework for VMAT/IMRT. To achieve high speed, we investigate the use of a simple convex formulation of the inverse treatment planning problem that takes advantage of recent developments in the field of distributed optimization. Methods: A Monte Carlo (MC) dose calculation algorithm was used to calculate the dose matrix (268228 voxels x 360 beams, 96M non-zeros) for a 360-aperture, 4-arc VMAT plan taken from the clinic. We wrote the objective for the inverse treatment planning problem as a sum of convex (piecewise-linear) penalties on the dose at each voxel in the planning volume. This convex voxel-separable formulation allowed us to apply a new, open-source, CPU- and GPU-capable optimization solver (http://foges.github.io/pogs/) to calculate our solutions of optimal beam intensities. In each planning session, after performing one full optimization we accelerated subsequent runs by “warm-starting”: for run k, the optimal solution from run k-1 was used as an initial guess. We implemented the treatment planning application as a Python web server running on a standard g2–2xlarge GPU node on Amazon EC2. Results: Our method formed optimal treatment plans in 5–15 seconds. Warm-start times ranged from 100ms–8s (mean 3s) while sweeping out a 5-log range of tradeoffs between target coverage and OAR sparing in 1000 total optimizations. Satisfactory plans were reached in 1–10 iterations of the optimization, with total planning time <10 minutes. Dosimetric characteristics such as the DVH curves showed that the resultant plans were comparable or superior to the clinically delivered plan. Conclusion: This work demonstrates the feasibility of high-quality, low-latency treatment planning using a convex problem formulation and GPU- based convex solver, making it practical to manipulate treatment objectives and view DVH curves and dose-wash views in nearly real-time in a web application. Funding support for this work is provided by the Stanford Bio-X Bowes Graduate Fellowship and NIH Grant 5R01CA176553