Is it possible to solve a quadratic cost function which is subject to both nonlinear (quadratic) & linear constriants by SQP methods? If not, what is the best iterative solution for this kind of problem?
Thanks
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Yes, you are looking for quadratically-constraint quadratic programming (QCQP).
You would solve your SQP as a sequential QCQP, (You can find results in literature for SQCQP). Most solvers come with a "SOCP"(Second-order cone program) solver - SOCP's subsume QP's and QCQP's.
For reference, as I know nothing about your actual problem domain - it's also often totally fair to take a first-order Taylor approximation of your constraints, just as you (presumably) took a second-order Taylor approximation of your cost function for your SQP.
An example of a paper that does that (in robotics) is Fossen's Constrainsed Nonlinear Control Allocation
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$\begingroup$ thanks jacob ...all i'm doubtfull about is lagrangian matrix in SQP which is combination of nonlinear (linearized) and linear Constraints which results into a singular matrix and not satisfy the SQP non-singularity Condition of Lagrangian matrix and by the way my field is target localization $\endgroup$– M.NitroNov 6 '15 at 17:43