HOPT – A MATLAB Package for Constrained Optimization in Hardy Spaces

where f̂k = ∫ π −π f(θ)e −ikθ dθ, k ∈ Z, are the Fourier coefficients of f . Further, we assume that g ∈ C(∂D) with g > 0, that K ⊂ ∂D is closed and has positive measure (in practice, K will be an interval or a collection of intervals on ∂D), and that φ ∈ C(K) with |φ| ≤ g on K. Finally, we assume that g, φ and K are symmetric, i.e., φ(e) = φ(e−iθ), g(e) = g(e), and K = K. Under these assumptions, the problem (H-OPTp) has a unique solution which is again symmetric, and the solution of the discetized version of (H-OPTp) (which is solved by this package) converges to the solution of (H-OPTp), see [4, 5].