RUI:  Computational Complexity of Continuous Functions
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Historically complexity theory has been concerned with the intrinsic            difficulty of problems whose underlying domain consists of the integers         or other discrete objects.  More recently, there is a growing interest          in understanding complexity issues arising in solving problems rooted           in continuous mathematics.  Here, in contrast to the discrete case, the         basic foundational questions are far from resolved.  Under                      investigation is the role the condition (or the logarithm of the                condition) of a problem plays in (1) formulating natural models of              computation and measures of complexity, and (2) designing algorithms,           for continuous problems.  The linear programming problem with its               various competing algorithms defined via disparate models of                    computation and complexity provides a rich source of ideas for this             investigation.
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