The primary objectives concern the development and analysis of algorithms for linear programming within a complexity theory motivated by functional analysis rather than the traditional motivated by algebra and combinatorics. Special attention is given to issues concerning computer round-off error and inexact data, issues such as how one might use the prior knowledge one has regarding the structure of the problem to be solved in order to efficiently solve the problem using less computational precision than would be needed otherwise. The use of iterative methods for solving the equations that arise when applying methods is investigated, as is the possibility that the algorithms are (nearly) optimal; optimality is investigated via approximation theory. Perturbation theory for linear programming is being developed. Certain notions which have proven useful in the context of linear programming are being investigated in a more general context multi-variate polynomials. It is intended that all of the investigations will be carried out with as much generality as is possible; for example, the cones defining non-negativity will not be required to be polyhedral.
