ROW: Algorithms in Polynomial Time for Convex Optimization
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The proposed research is to establish a class of polynomially bounded           algorithms for solving convex programming problems efficiently.  The            work is to focus on classical barrier methods, such as the Sequential           Unconstrained Minimization Technique (SUMT) and it's variants.                  Specifically, " Projective SUMT " is one such variant that is derived           from the barrier function method by utilizing the differential                  equation characterizing the trajectory of unconstrained minimizers.             The assumptions for convergence of these barrier-type methods are               considerably weaker than those proposed by Karmarkar.                                                                                                           The concept of factorable functions wil be used in the analysis of              running time.  Representation of a function as factorable enables the           automatic calculation of higher order derivatives, and can be useful            for encoding the data and function calculations.  The running time              also depends upon the time required to solve a system of equations              with respect to the Hessian of the suitable factorable barrier                  function, the solution of an approximate step-size problem, and the             number of iterations required to find the solution to prescribed                accuracy.  These issues will be explored in the research.
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