A Mixed Line Search Smoothing Quasi-Newton Method for Solving Linear Second-Order Cone Programming Problem | Zendy

Zhuqing Gui | Zendy; Chunyan Hu | Zendy; Zhibin Zhu | Zendy

AI Assistant Blog Pricing

Home ZAIA Blog

Open Access

A Mixed Line Search Smoothing Quasi-Newton Method for Solving Linear Second-Order Cone Programming Problem

Author(s) -

Zhuqing Gui,

Chunyan Hu,

Zhibin Zhu

Publication year - 2013

Publication title -

isrn operations research

Language(s) - English

Resource type - Journals

ISSN - 2314-6397

DOI - 10.1155/2013/230717

Subject(s) - karush–kuhn–tucker conditions , line search , smoothing , mathematics , nonlinear programming , mathematical optimization , first order , convergence (economics) , nonlinear system , order (exchange) , jordan algebra , complementarity (molecular biology) , newton's method , mixed complementarity problem , line (geometry) , algebra over a field , computer science , pure mathematics , algebra representation , path (computing) , geometry , economic growth , quantum mechanics , programming language , statistics , physics , finance , economics , genetics , biology

Firstly, we give the Karush-Kuhn-Tucker (KKT) optimality condition of primal problem and introduce Jordan algebra simply. On the basis of Jordan algebra, we extend smoothing Fischer-Burmeister (F-B) function to Jordan algebra and make the complementarity condition smoothing. So the first-order optimization condition can be reformed to a nonlinear system. Secondly, we use the mixed line search quasi-Newton method to solve this nonlinear system. Finally, we prove the globally and locally superlinear convergence of the algorithm.

The content you want is available to Zendy users.

Already have an account? Click here to sign in.

Having issues? You can contact us here

Accelerating Research