As mentioned earlier, we use the Charnes-Cooper transformation to change the nonconvex fractional QCQP into convex problem.
Complexity of interior points methods, which are usually used in QCQP optimization problems, is O((R + 1)ln(1/[epsilon])) , where [epsilon] is the accuracy and (R + 1) is the size of problem.
Farina, "Fractional QCQP with applications in ML steering direction estimation for radar detection," IEEE Transactions on Signal Processing, vol.
we make use of this norm constrain to calculate optimal radius of the uncertainty set; this suboptimal equation is in the form of quadratic programming quadratically constrained problem (QCQP
To obtain the convex relaxation of the nonconvex QCQP
problem (22), we relax the equation T = [beta][[beta].sup.T] to T [greater than or equal to] [beta][[beta].sup.T], which can be equivalently expressed by the constraint in (27) according to the Schur complement lemma .
In this paper, a QP-free algorithm without solving any QP and QCQP
subproblems is presented for unconstrained nonlinear finite minimax problems.
The subproblem to determine [W.sub.r] with given fixed T, R and [W.sub.l], [for all]l [not equal to] r is QCQP, which is well known to belong to the categories of convex optimization problem.
This subproblem is QCQP since the objective function is quadratic over T and quadratic constraints on T are given.
The subproblem to determine T with given fixed W and R is QCQP, which is a convex problem.