Abstract
A class Ψ of strictly concave and twice continuously differentiable functions ψ: R → R with particular properties is used for constraint transformation in the framework of a Nonlinear Rescaling (NR) method with “dynamic” scaling parameter updates. We show that the NR method is equivalent to the Interior Quadratic Prox method for the dual problem in a rescaled dual space.The equivalence is used to prove convergence and to estimate the rate of convergence of the NR method and its dual equivalent under very mild assumptions on the input data for a wide class Ψ of constraint transformations. It is also used to estimate the rate of convergence under strict complementarity and under the standard second order optimality condition.We proved that for any ψ ∈ Ψ, which corresponds to a well-defined dual kernel ϕ = −ψ*, the NR method applied to LP generates a quadratically convergent dual sequence if the dual LP has a unique solution.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
