sci.op-research

Hello folks,

I am dealing a convex quadratic problem in some variables, say x_i's
and some constants a_k's. The constants a_k's are themselves the
solution of another convex quadratic problem (which does not involve
x_i's), so I call it nested programming.

A naive attempt to solve this system is to find a closed form solution
for the inner program (the one in a_k's) and the plug its solution in
the outer program (the one in x_i's) and solve it again. Unfortunately
closed form solution looks nasty in my case, due to constraints a_k>0,
the stationary points of the lagrangian is of form a_k=0 or
a_k=something_else, which is a disjunctive constraint and cannot be
used in the other program.

Is there any way other than closed form solution idea to solve a
nested program like this? Is any trick such as introducing auxilary
variables and additional terms possible here?

Thank you in advance!

G.D.