We set out an object localization scheme based on a convex programming matching method. The proposed approach is designed to match general objects, especially objects with very little texture, and in strong background clutter; traditional methods have great difficulty in such situations. We propose a convex quadratic programming (CQP) relaxation method to solve the problem more robustly. The CQP relaxation uses a small number of basis points to represent the target point space and therefore can be used in very large scale matching problems. We further propose a successive convexification scheme to improve the matching accuracy. Scale and rotation estimation is integrated as well so that the proposed scheme can be applied to general conditions. Experiments show very promising results for the proposed method in object localization applications.