Abstract
We introduce a feasible corrector–predictor interior-point algorithm (CP IPA) for solving linear optimization problems which is based on a new search direction. The search directions are obtained by using the algebraic equivalent transformation (AET) of the Newton system which defines the central path. The AET of the Newton system is based on the map that is a difference of the identity function and square root function. We prove global convergence of the method and derive the iteration bound that matches best iteration bounds known for these types of methods. Furthermore, we prove the practical efficiency of the new algorithm by presenting numerical results. This is the first CP IPA which is based on the above mentioned search direction.
Highlights
Karmarkar (1984) presented the first projective IPA for solving LO problems with polynomial-time complexity
Darvay (2005, 2009) introduced PC IP√As for LO that are based on the algebraic equivalent transformation (AET) technique and he used the function ψ(t) = t with domain Dψ = (0, ∞) in order to determine the transformed central path and the modified Newton system
We use the AET method for t√he system which defines the central path that is based on the function ψ(t) = t −
Summary
Karmarkar (1984) presented the first projective IPA for solving LO problems with polynomial-time complexity. IPAs. In theory, short-update algorithms give usually more efficient theoretical results with simpler analysis, while in practice, the large-step versions perform generally better. Darvay (2005, 2009) introduced PC IP√As for LO that are based on the AET technique and he used the function ψ(t) = t with domain Dψ = (0, ∞) in order to determine the transformed central path and the modified Newton system. We use the AET method for t√he system which defines the central path that is based on the function ψ(t) = t −. We present some numerical results and we compare our CP IPA with the classical primal-dual method, which is based on the same search direction and uses only one step in each iteration.
Sign-in/Register to view highlights & summary 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.
