The problem of designing novel process systems for deployment in extreme and hostile environments is addressed. Specifically, the process system of interest is a subsea production facility for ultra deepwater oil and gas production. The costs associated with operational failures in deepwater environments are prohibitively high and therefore warrant the application of worst-case design strategies. That is, prior to the construction and deployment of a process, a certificate of robust feasibility is obtained for the proposed design. In this paper, the concept of worst-case design is addressed by formulating the design feasibility problem as a semi-infinite optimization problem with implicit functions embedded. A basic model of a subsea production facility is presented for a case study of rigorous performance and safety verification. Relying on recent advances in global optimization of implicit functions and semi-infinite programming, the design feasibility problem is solved, demonstrating that this approach is effective in addressing the problem of worst-case design of novel process systems. © 2014 American Institute of Chemical Engineers AIChE J, 2014