This Small Business Innovation Research Phase I project will address the challenges of large-scale nonlinear optimization in the presence of discrete elements. Building on previous success with an integrated approach to classical, smooth nonlinear optimization, the goal of this research will be to derive and implement large-scale general-purpose methods for nonlinear optimization over (i ) integer-valued decision variables via a branch-and-bound approach, and (ii ) complementarity constraints using a direct penalty approach. Anticipated applications will encompass engineering problems such as process synthesis, network planning, optimal power flow, and integrated circuit design, as well as decision problems in such areas as power capacity planning and strategic bidding. The commercial potential of the research will be demonstrated by tests on real applications contributed by users of the proposing company's current nonlinear optimization software
