For centuries, ordinary differential equations with smooth input functions have routinely been used for modeling, analysis, and design of physical and engineering systems. However, these equations are vastly inadequate to deal with many naturally occurring engineering problems that contain inequalities (for modeling unilateral constraints) and disjunctive conditions (for conditional phenomena including hybrid systems).

The DaVinci project brings together mathematicians and engineers to address the urgent need for a thorough understanding of the mathematics of engineering systems that can be modeled by Differential Algebraic Inequalities and Differential Complementarity Problems. The project will open a new chapter in applied mathematics in which classical differential equation theory is merged with contemporary mathematical programming methods. The deliverables of our research are a set of broadly applicable mathematical theories, algorithms, and computational tools that will have a direct impact on an array of engineering and scientific disciplines."

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Last Updated: August 12th, 2003