[Ipopt] Mehrotra's predictor-corrector algorithm

zjuzw at sohu.com zjuzw at sohu.com
Fri Mar 15 06:05:45 EDT 2013

Firstly,thank you for your interest in this E-mail.On the website http://www.coin-or.org/Ipopt/documentation/node105.html presents how to reset option "mehrotra_algorithm".
If option "mehrotra_algorithm" sets to "yes",Ipopt runs as Mehrotra's predictor-corrector 
algorithm.This automatically disables the line search, and chooses the (unglobalized) adaptive 
mu strategy with the "probing" oracle, and uses "corrector_type=affine" without any safeguards;
you should not set any of those options explicitly in addition.So in my opinion,only reseting 
option "mehrotra_algorithm yes" equals to reseting options "mu_strategy adaptive"+"mu_oracle probing"
+"corrector_type affine",but different iteration processing appeared when solving nonlinear optimization
problems under aforementioned two configuration,and the former manifests worse results.Can someone 
explain this phenomenon for me? 
The second question: In the paper "Adaptive Barrier Strategies for Nonlinear Interior Methods" part 7 
"Corrector Steps" presents Mehrotra's predictor-corrector(MPC) algorithm in detail,points out the complete
MPC step is the sum of the primal-dual and corrector steps. Here,in IPOPT,keyword "corrector_type" has three
options "none,affine,primal-dual",what's the difference between affine and primal-dual,in that paper only 
presents one type of method to calculate corrector step.
The third question: Also in that paper part 5 "A Globalization Method".As long as the adaptive primal-dual 
steps make sufficient progress towards the solution, the algorithm is free to choose a new value for the 
barrier parameter at every iteration. We call this the free mode. However, if the iteration fails to maintain 
progress, then the algorithm reverts to a monotone mode, in which a Fiacco-McCormick strategy is applied. 
Here, the value of the barrier parameter remains fixed, and a robust globalization technique (e.g., based ona merit function or a filter) is employed to ensure progress for the corresponding barrier problem. Once the 
barrier problem is approximately minimized, the barrier parameter is decreased. The monotone mode continues 
until an iterate is generated that makes sufficient progress for the original problem, at which point the free mode resumes. Does this globalization procedure apply in current version of IPOPT?
Sincerely,From Wei.
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