This paper presents a new framework for solving geometric structure and motion problems based on L_∞ -norm. Instead of using the common sum-of-squares cost-function, that is, the L_₂ -norm, the model-fitting errors are measured using the L_∞ -norm. Unlike traditional methods based on L_₂, our framework allows for efficient computation of global estimates. We show that a variety of structure and motion problems, for example, triangulation, camera resectioning and homography estimation can be recast as a quasi-convex optimization problem within this framework. These problems can be efficiently solved using Second Order Cone Programming (SOCP) which is a standard technique in convex optimization. The proposed solutions have been validated on real data in different settings with small and large dimensions and with excellent performance.