Unsubscribe On Wed, Jan 11, 2023 at 8:48 AM Ray Daniel Zimmerman <[email protected]> wrote:
> I’m afraid I don’t have anything very concrete to offer in response to > your questions … but in my experience also I’ve been surprised at how well > the primal-dual interior point method converges even in the presence of > fairly ill-conditioned matrices. > > My only suggestion in terms of approaches to wok around the > ill-conditioning would be to look for papers by the authors of the Artelys > Knitro and IPOPT packages which use similar algorithms, to see what > approaches they have implemented to deal with ill-conditioning. I don’t > have the reference handy, but I’m pretty sure I saw such a paper by the > creators of Knitro. > > There are probably others on this list with more experience and expertise > on this issue. > > Ray > > > > On Jan 9, 2023, at 9:42 PM, Min Zhou <[email protected]> wrote: > > > > Dear Ray; > > > > I am a Ph.D. student working on power system optimization and have > > been matpower to solve optimal power flow problems recently. However, > > I got the following questions when I was running the algorithm: > > > > 1. In Newton's step, we need to solve a set of equations Ax = b. I > > found that the condition number of matrix A is very large (about 1e8). > > Thus, A is ill-conditioned. I was wondering why Newton's method can > > still get good numerical performance even when the equation Ax = b is > > ill-conditioned. Is 1e8 an acceptable condition number for Newton's > > method? > > > > 2. Is there any approach to solve the ill-condition problem of > > Newton's method when solving AC-OPF? > > > > Thank you for your time and consideration. > > -- > > Min ZHOU > > School of Data Science > > City University of Hong Kong > > > >
