Solving oligopolistic equilibrium problems with convex optimization

•General approach to solve imperfect partial equilibrium problems as convex optimization problems.•Construct convex problems with identical Karush–Kuhn–Tucker conditions as a Cournot oligopoly.•The approach generalizes to conjectural variation models, stochastic models, etc.•Dramatic reductions in both model development and solution times.•Solve partial equilibrium models orders of magnitude faster than the state-of-the-art.