Semidefinite Programming: Optimality Conditions and Stability

2012 ◽  
Keyword(s):  
Semidefinite Programming ◽  
Optimality Conditions

scholarly journals PREDICTOR–CORRECTOR SMOOTHING NEWTON METHOD FOR SOLVING SEMIDEFINITE PROGRAMMING

2009 ◽  
Vol 79 (3) ◽  
pp. 367-376
Author(s):  
CAIYING WU ◽  
GUOQING CHEN
Keyword(s):  
Global Convergence ◽  
Semidefinite Programming ◽  
Optimality Conditions ◽  
Newton Method ◽  
Superlinear Convergence ◽  
Smoothing Newton Method ◽  
Equivalent Transformation ◽  
Newton Algorithm ◽  
Smoothing Methods ◽  
Predictor Corrector

AbstractThere has been much interest recently in smoothing methods for solving semidefinite programming (SDP). In this paper, based on the equivalent transformation for the optimality conditions of SDP, we present a predictor–corrector smoothing Newton algorithm for SDP. Issues such as the existence of Newton directions, boundedness of iterates, global convergence, and local superlinear convergence of our algorithm are studied under suitable assumptions.

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