https://en.wikipedia.org/   has an article on it and even better, google is your friend:

a search with ''nonlinear complementarity problem" will give you a lot (maybe too much) of information.

the guide

http://plato.asu.edu/guide.html

also points you to information, namely Michael Ferris homepage, who did a lot of work on it.  The main trouble with the problem: one cannot reformulate it routinely as a nonlinear programming problem since in this form it violates important regularity assumptions.

These articles may be helpful, you can also see in the references you may find earlier and more simple articles.

Best Luck.

http://www.sciencedirect.com/science/article/pii/S0377042700002624/pdfft?md5=492a8f5a04513834e0d15c1c3abd2b33&pid=1-s2.0-S0377042700002624-main.pdf

https://www.google.com.sa/url?sa=t&rct=j&q=&esrc=s&source=web&cd=4&cad=rja&uact=8&ved=0ahUKEwjcm6_P2f_KAhXI0xoKHQLdBkoQFgg4MAM&url=http%3A%2F%2Fwww-personal.umich.edu%2F~murty%2FLCPart.pdf&usg=AFQjCNFTj28B6y0r-YdEIEwhkMaXJbkj1A&sig2=d0mwB9U3H2exKD3MSC5lvQ

https://www.google.com.sa/url?sa=t&rct=j&q=&esrc=s&source=web&cd=5&cad=rja&uact=8&ved=0ahUKEwjcm6_P2f_KAhXI0xoKHQLdBkoQFghDMAQ&url=http%3A%2F%2Fpages.cs.wisc.edu%2F~ferris%2Ftalks%2Fbaltimore.pdf&usg=AFQjCNEkdzr-E5Z6RJRTHJohE8QMPat20Q&sig2=RJTH5T8aOGbJfOm4UCeEUA

https://www.google.com.sa/url?sa=t&rct=j&q=&esrc=s&source=web&cd=7&cad=rja&uact=8&ved=0ahUKEwjcm6_P2f_KAhXI0xoKHQLdBkoQFghUMAY&url=http%3A%2F%2Flink.springer.com%2Farticle%2F10.1007%252FBF00927414&usg=AFQjCNHhloAjQNKr4ZGs66RMnXf1586YoQ&sig2=R-MY4U8aSeyooCQz2Qf3xg

https://www.google.com.sa/url?sa=t&rct=j&q=&esrc=s&source=web&cd=10&cad=rja&uact=8&ved=0ahUKEwjcm6_P2f_KAhXI0xoKHQLdBkoQFgh0MAk&url=http%3A%2F%2Fwww.math.nus.edu.sg%2F~matsundf%2FAMO_99.pdf&usg=AFQjCNFI8pHstxmLuIx5atQNj9DGzoaeiA&sig2=7Kojd09fVFCjZB1giyKzYQ

These may be helpful too:

www.sciencedirect.com/science/article/pii/0022247X87903234

ftp://ftp.dis.uniroma1.it/facchinei/papers94/P2_94.ps.Z

link.springer.com/article/10.1186%2Fs13660-015-0781-6