New Approaches to Linear and Nonlinear Programming
Final rept. 1 Mar 1987-28 Feb 1989
STANFORD UNIV CA DEPT OF OPERATIONS RESEARCH
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The project involves study of the theoretical properties and computational performance of techniques that solve linear and nonlinear programs by means of nonlinear transformations. The group at the Systems Optimization Laboratory SOL were the first to recognize the connection between Karmarkars 1984 projective method and the logarithmetic barrier method see Gill, Murray, Saunders, Tomlin and Wright, 1986. It is now generally recognized that essentially all interior-point methods for linear programming inspired by Karmarkars method are closely related to application of Newtons method to a sequence of barrier functions see e.g., Gonzaga, 1987 Renegar, 1988, Anstreicher, 1988. Each barrier function is defined from the objective function and a barrier term that is infinite along the boundary of the feasible region. As the weight on the barrier term is reduced to zero, the solution of the subproblem becomes closer to the solution of the original problem.
- Operations Research