Write a MATLAB code to solve the following W-weighted version of the nearest correlation matrix problem min 1 2kG-Xk2 W s.t. Xii = 1, i = 1,â€¦,n, X 0,

NATIONAL UNIVERSITY OF SINGAPORE Department of Mathematics Semester II (2016/2017) MA5232 Modeling and Numerical SimulationsAssignments on the Optimization Part
Write a MATLAB code to solve the following W-weighted version of the nearest correlation matrix problem
min
1 2kG-Xk2 W s.t. Xii = 1, i = 1,â€¦,n, X 0,
(1)
where W ?Sn is symmetric and positive de?nite and for any Y ?Sn, kYkW = kW1/2Y W1/2k.
Note that when W = I, problem (1) has been solved by a quadratically convergent semismooth Newton method in [1] and the corresponding code with the name CorrelationMatrix.m can be found at http://www.math.nus.edu.sg/fmatsundf/. For the general W-weighted case, you may also ?nd a preliminary version code called CorNewton3-Wnorm.m from the same website. You may use this preliminary code, but you need to make it to be as e?cient as CorrelationMatrix.m if W happens to be very close to the identity matrix I. Submit your code electronically via IVLE with the ?rst line of the output reading as This is the code written by YOUR NAME together with a ?le documenting the method that you use. To avoid confusions, please zip all your ?les into one ?le and submit to the AssignmentIII(Optimization) folder. I will particularly test your code based on the following criteria:
â€¢ Speed: the faster the better â€¢ Memory requirements: the smaller the better â€¢ Robustness: it should work well for a large class of problems â€¢ Preconditioning: to solve a large system needs a good pre-conditioner â€¢ Readability: make it easier to read
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References
[1] H.D. Qi and D.F. Sun, A quadratically convergent Newton method for computing the nearest correlation matrix, SIAM Journal on Matrix Analysis and Applications 28 (2006) 360â€“385.

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