Is it possible to adapt the active set method for solving nonlinear problems with non-quadratic function and linears constraints?
The applicability of an active set method does not hinge on the nonlinearity of the objective function; it is a more important factor how constraints are defined, as convergence hinges on the possibility to create feasible subproblems based on an approximation of the constraints around the current point. So, for example, it is important that the constraints are defined by differentiable functions. This is laid out very clearly by a colleague and expert in nonlinear programming here:
http://people.duke.edu/~hpgavin/SystemID/References/Gill-SQP-Active-2011.pdf
Yes, it is.
The scheme is called Sequential Quadratic Programming (SQP).
Nonlinear programs are approximated by a sequence of quadratic programs.
The exists efficient and reliable implementations of SQP, for example:
http://www.mcs.anl.gov/~leyffer/solvers.html
http://web.stanford.edu/group/SOL/papers/SNOPT-SIGEST.pdf
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