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Abstract: We present a generalization of the Penalty/Barrier Multiplier algorithm for the semidefinite programming, based on a matrix form of Lagrange multipliers. Our approach allows to use among others logarithmic, shifted logarithmic, exponential and a very effective quadratic-logarithmic penalty/barrier functions. We present dual analysis of the method, based on its correspondence to a proximal point algorithm with nonquadratic distance-like function. We give computationally tractable dual bounds,... (Update)
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...problem becomes more difficult for optimization. As a minimization procedure we used the Newton method with frozen Hessian (see for example [15]) At each iteration the Hessian matrix was computed and 292 Maximum correlation approach Method Mean squared Std. deviation error of...
...value of the penalty parameter. We should mention, that PBM approach was extended [8] for Semidefinite Programming and successfully applied [4] for various real life large scale problems. 2.1 Computational complexity of Newton step The main computational effort of PBM method is...
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BibTeX entry: (Update)
L. Mosheyev and M. Zibulevsky, "Penalty/barrier multiplier algorithm for semidefinite programming," Optimization Methods and Software, 1999. http://citeseer.ist.psu.edu/mosheyev99penaltybarrier.html More
@techreport{ mosheyev99penaltybarrier,
author = "L. Mosheyev and M. Zibulevsky",
title = "Penalty/Barrier Multiplier Algorithm for Semidefinite Programming",
address = "Albuquerque, NM 87131",
year = "1999",
url = "citeseer.ist.psu.edu/mosheyev99penaltybarrier.html" }
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