Network management on multi-tenant container-based data centers has critical impact on performance. Tenants encapsulate applications in containers abstracting away details on hosting infrastructures, and entrust data centers management framework with the provisioning of network QoS requirements. In this paper, we propose a network-aware multi-criteria container scheduler to jointly process containers and network requirements. We introduce a new Mixed Integer Linear Programming formulation for network-aware scheduling encompassing both tenants and providers metrics. We describe two GPU-accelerated modules to address the complexity barrier of the problem and efficiently process scheduling requests. Our experiments show that our scheduling approach accounting for both network and containers outperforms traditional algorithms used by containers orchestrators.