Results 1 
1 of
1
A Stable PrimalDual Approach for Linear Programming
"... This paper studies a primaldual interior/exteriorpoint pathfollowing approach for linearprogramming that is motivated on using an iterative solver rather than a direct solver for the search direction. We begin with the usual perturbed primaldual optimality equations Fu(x, y, z) = 0. Under nonde ..."
Abstract

Cited by 2 (1 self)
 Add to MetaCart
(Show Context)
This paper studies a primaldual interior/exteriorpoint pathfollowing approach for linearprogramming that is motivated on using an iterative solver rather than a direct solver for the search direction. We begin with the usual perturbed primaldual optimality equations Fu(x, y, z) = 0. Under nondegeneracy assumptions, this nonlinear system is wellposed,i.e. it has a nonsingular Jacobian at optimality and is not necessarily illconditioned as the iterates approach optimality. We use a simple preprocessing step to eliminate boththe primal and dual feasibility equations. This results in a single bilinear equation that maintains the wellposedness property. We then apply both a direct solution techniqueas well as a preconditioned conjugate gradient method (PCG), within an inexact Newton framework, directly on the linearized equations. This is done without forming the usualnormal equations, NEQ, or augmented system. Sparsity is maintained. The work of aniteration for the PCG approach consists almost entirely in the (approximate) solution of this wellposed linearized system. Therefore, improvements depend on efficient preconditioning.