Stability and accuracy of inexact interior point methods for convex quadratic programming
Inexact interior point (IP) methods are procedures for linear, convex and nonlinear programming problems where the linear system arising at each iteration is solved approximately. This paper considers primal-dual IP methods where the linear system arising at each iteration is formulated in the reduced (augmented) form and solved approximately. This work analyses the accuracy of the so-called inexact step, i.e., the step that solves the unreduced system, when combining the effects of both different levels of accuracy in the inexact computation and different processes for retrieving the step after block elimination. The paper considers the sources of inexactness due either to roundoff and computational errors or to the iterative solution of the augmented system using typical procedures. If inexactness refers to roundoff errors, the presented theory recovers and extends some known results.
scientific article; zbMATH DE number 6819193
scientific article