In this paper, we propose a novel trajectory optimization algorithm for\nmobile manipulators under end-effector path, collision avoidance and various\nkinematic constraints. Our key contribution lies in showing how this highly\nnon-linear and non-convex problem can be solved as a sequence of convex\nunconstrained quadratic programs (QPs). This is achieved by reformulating the\nnon-linear constraints that arise out of manipulator kinematics and its\ncoupling with the mobile base in a multi-affine form. We then use techniques\nfrom Alternating Direction Method of Multipliers (ADMM) to formulate and solve\nthe trajectory optimization problem. The proposed ADMM has two similar\nnon-convex steps. Importantly, a convex surrogate can be derived for each of\nthem. We show how large parts of our optimization can be solved in parallel\nproviding the possibility of exploiting multi-core CPUs/GPUs. We validate our\ntrajectory optimization on different benchmark examples. Specifically, we\nhighlight how it solves the cyclicity bottleneck and provides a holistic\napproach where diverse set of trajectories can be obtained by trading-off\ndifferent aspects of manipulator and mobile base motion.\n