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There is now a CONTENT FREEZE for Mercury while we switch to a new platform. It began on Friday, March 10 at 6pm and will end on Wednesday, March 15 at noon. No new content can be created during this time, but all material in the system as of the beginning of the freeze will be migrated to the new platform, including users and groups. Functionally the new site is identical to the old one. webteam@gatech.edu
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First we review the basic concepts of self-regular proximity based Interior Point Method that allowed a complexity improvement of large-update, large-scale interior point methods. Some intriguing properties of a specific self-regular proximity function are discussed and we will show that the neighborhood used in our predictor-corrector algorithm contains the infinity norm neighborhood that is used in all practical implementations of IPMs.
Then a new adaptive self-regular predictor-corrector algorithm is presented where the corrector step is defined by our self-regular proximity and the predictor step is either a self-regular or an affine-scaling step. Polynomial worst case complexity [O(sqrt(n) log(n) L) in the best case] and asymptotic quadratic convergence rate is established.
