arXiv:2611.06850v1 Announce Type: new Abstract: Fixed-order frequency-weighted H-infinity approximation is a nonconvex problem, and local optimization methods can be sensitive to initialization. We present extremal-phase-guided sequential convex optimization (EPGSCO) for stable fixed-order rational approximation. We introduce a novel phase-guidance technique motivated by the all-pass structure underlying optimal Hankel-norm approximation, with a phase template fitted to the error-magnitude derivative at dominant peaks. We integrate this guidance with dominant-peak selection, focused frequency grids, and adaptive pole-residue and polynomial-coefficient updates to address stagnation and improve approximation accuracy. CD-player examples and benchmarks with known optimal errors evaluate the algorithm against established methods. Comparisons with classical sequential convex optimization (SCO) under shared settings for the common components assess the combined contribution of phase guidance and adaptive frequency refinement. Results demonstrate improved accuracy in most of the tested cases and attainment of the known optimum from four tested initializations for a constructed order-42 benchmark, with additional computation in some cases.