Boggs, Domich, and Rogers remain active participants in the theoretical and computational aspects of the ongoing worldwide research on methods for solving the linear programming and quadratic programming problems. They have obtained excellent results with an interior point method that is applicable for solving a general class of such problems that is not currently solved by the primal dual methods being examined by other researchers. Their approach combines several individual search directions to produce an optimal step at each iteration. Their original work, developed for LP, is an effective method that is competitive with the best of the LP algorithms developed elsewhere. Their QP approach has few, if any, competitors in terms of robustness and size of problems that can be efficiently handled. Their procedure, O3D, is applicable for problems arising in the context of airline scheduling, pooling and blending in chemical engineering, heat exchanger and chemical reactor networks, optimal control, mechanical design, entropy, and nonconvex energy optimization. It also has application in sequential quadratic programming codes for solving nonlinear programming problems (NLP).
During this past year, Rogers tested and integrated a newly developed sparse matrix ordering procedure and a supernode factorization procedure into a Fortran 90 version of O3D. This work has substantially reduced the memory and time requirements of this procedure, a critical improvement in making the code applicable to solving the object oriented programs of the geophysical industry that is expected to be one of its major users. The code should be ready for release by the end of the year.
A manuscript describing this work has been accepted for publication in the Annals of Operations Research special volume on Interior Point Methods for Mathematical Programming. It was also presented at the 15th International Symposium on Mathematical Programming in Ann Arbor, Michigan, and at the University of Colorado Computer Science Department Numerical Analysis Seminar, in Boulder, Colorado.