Enlarging neighborhoods of interior-point algorithms for linear programming via least values of proximity measure functions
The interior-point algorithms working in wider neighborhoods are generally known to perform better than those counterparts using smaller neighborhoods. The author considers predictor-corrector methods based on a 2-norm and an \({\infty}\)-norm neighborhood, and shows how to use the least value of a proximity measure function to enlarge the neighborhood of the central path. The algorithms are proved to retain both the best known iteration complexity and the quadratic convergence of the original algorithms. The methods can be viewed as a new design for interior-point methods.
scientific article; zbMATH DE number 5173639