Case Studies for a First-Order Robust Nonlinear Programming Formulation

In this paper, we conduct three case studies to assess the effectiveness of a recently proposed first-order method for robust nonlinear programming [Zhang, Y.: J. Optim. Theory Appl. 132, 111–124 (2007)]. Three robust nonlinear programming problems were chosen from the literature using the criteria that results calculated using other methods must be available and the problems should be realistic, but fairly simple. Our studies show that the first-order method produced reasonable solutions when the level of uncertainty was small to moderate. In addition, we demonstrate a method for leveraging a theoretical result to eliminate constraint violations. Since the first-order method is relatively inexpensive in comparison to other robust optimization techniques, our studies indicate that, under moderate uncertainty, the first-order approach may be more suitable than other methods for large problems. The authors recognize funding from NSF Grants DMS-0405831 and DMS-0240058.