## Iterative solutions using quadratic programming

The problem (1.42) can be locally approximated with a convex QP problem by assuming that:

1. the power consumption can be approximated by a quadratic term in f, near the last force f0 such that f = f0 + Af.

2. the singularity avoidance penalty can be approximated by a linear term linearized about the last azimuth angle a0 such that a = a0 + Aa.

The resulting QP criterion is (Johansen et al., 2004):

da s + det(T(a)W-1TT (a)) subject to s + TK)Af + da(T(a)f ))f Aa = t — Tfoft fmin — f0 < f < fmax — f " "

amin — a0 < Aa < amax — a0 Aamin < Aa < Aamax

The convex QP problem (1.43) can be solved by using standard software for numerical optimization.

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