Geometric reconstruction problems in computer vision are often solved by minimizing a cost function that combines the reprojection errors in the 2D images. In this paper, we show that, for various geometric reconstruction problems, their reprojection error functions share a common and quasiconvex formulation. Based on the quasiconvexity, we present a novel quasiconvex optimization framework in which the geometric reconstruction problems are formulated as a small number of small-scale convex programs that are ready to solve. Our final reconstruction algorithm is simple and has intuitive geometric interpretation. In contrast to existing random sampling or local minimization approaches, our algorithm is deterministic and guarantees a predefined accuracy of the minimization result. We demonstrate the effectiveness of our algorithm by experiments on both synthetic and real data.