New Approaches to Linear and Nonlinear Programming
Abstract
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 Karmarkar's (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 Karmarkar's method are closely related to application of Newton's 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.
Document Details
- Document Type
- Technical Report
- Publication Date
- Dec 01, 1989
- Accession Number
- ADA224328
Entities
People
- Michael Saunders
- Walter Murray
Organizations
- Stanford University