Machine learning has tremendously benefited from graphics processing units (GPUs) to accelerate training and inference by several orders of magnitude. However, this success has not been replicated in general and exact combinatorial optimization. Our key contribution is to propose a general-purpose discrete constraint programming solver fully implemented on GPU. It is based on integer interval bound propagation and backtracking search. The two main ingredients are (1) ternary constraint network optimized for GPU architectures, and (2) an on-demand subproblems generation strategy. Our constraint solving algorithm is significantly simpler than those found in optimized CPU constraint solvers, yet is competitive with sequential solvers in the MiniZinc 2024 challenge.