Ever-increasing proliferation of the multimedia applications on the wireless LANs (WLANs) demands high-throughput transmission support from these networks which in turn necessitates efficient resource allocation approaches. The latest standard of the WLANs is the IEEE 802.11ac that leverages several physical layer techniques including downlink (DL) multiuser (MU) transmission to provide throughput requirement of the multimedia applications. This paper addresses video-cognizant joint scheduling and link adaptation problem in the IEEE DL MU 802.11ac. This problem is formulated according to the network utility maximization framework taking into account multimedia applications requirements and physical layer specification of the IEEE 802.11ac DL MU. The formulated problem is a non-convex problem due to the non-concave objective function and also non-convex constraints. A two-staged approach is proposed to solve it. In the first stage, the objective function is successively approximated by a concave function. In the second stage, in spite of the non-convex constraints, exploiting zero duality gap the problem is solved in the dual domain by means of a stochastic learning method. Since solving the dual problem involves an NP -hard subproblem, we design an ant colony based meta-heuristic to conquer it. The simulation results generated by the IEEE 802.11ac channel and physical layer models under the high efficiency video coding (HEVC) traffic substantiate the convergence of the proposed scheme to the required throughput of each video stream.