Conference rusure::math

1966.0. "A Problem on Lipschitz Continuity" by PASTA::SUDHARSANAN () Tue Apr 18 1995 21:37

 
Let M be an n by n real matrix, x be an n-length column vector, and
a(x) be a vector with each element a_i(x_i) - a bounded, strictly
monotonic, C-infinity function.  Consider the following equations


		x = M a(x) +  c

		y = u'x 

where c and u are n-length column vectors and y is a scalar.  
Allow the elements of M to be a vector mu of length n times n.  

When is the partial derivative of y with respect to mu 
Lipschitz on mu?  Are there particular matrix properties that M
has to satisfy for this? 


The above equations arise in some circuit problems as described
by A.N. Wilson, Nonlinear Networks: Theory and Analysis.  The
specific problem occurs when certain circuit parameters are to 
be changed to obtain desirable performance.  


S. Sudharsanan

sudharsanan@pasta.enet.dec.com