Please advise a reference to paper/book/sources with description of Complex value test functions for optimization like extended Rosenbrock or Powell? There are many analytical functions for testing non-linear/optimization algorithms but I was able to find only cases for real numbers. So the question is how to test a case when Jacobian/residual are complex value matrix/vector?
You can look into the following Book:
Complex Valued Matrix Derivatives : With applications in Signal processing and Communication, by Are Hjorungnes.
Hi,
I suggest you see the links on the topic.
Article Research on Rosenbrock Function Optimization Problem Based o...
Article A Numerical Study of Applying Complex-step Gradient and Hess...
https://www.csie.ntu.edu.tw/~r97002/temp/num_optimization.pdf
https://arxiv.org/pdf/1308.4008.pdf
https://www.sfu.ca/~ssurjano/optimization.html
https://spiral.imperial.ac.uk/bitstream/10044/1/22563/2/Rowe-AD-1975-PhD-Thesis.pdf
https://fse.studenttheses.ub.rug.nl/17777/1/bMATH_2018_MaquelinEI.pdf
https://optimization-online.org/wp-content/uploads/2012/03/3382.pdf
Best regards
Mohamed-Mourad Lafifi Debopam Ghosh Thank you for references. I looked into it quickly. Besides the fact that some papers really good it seems there is no apparent analytical test function C^n->C^n
I understand that after some math borrowed from Are Hjørungnes book(or similar) applied one could deduce some results from combination of analytical functions R^n->R^n but I hoped that someone already did it before
Maybe I just go wrong direction. I have some optimization workflow and before apply it to some frequency domain problem I wanted to test it with some analytical setup. Probably I should think about other ways to do it