{"ID":6497746,"CreatedAt":"2026-07-13T01:19:40.13847098Z","UpdatedAt":"2026-07-14T01:36:59.12045529Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2607.09254","arxiv_id":"2607.09254","title":"On feasibility problems with spectral constraints","abstract":"We study matrix feasibility problems \"find X in K intersect C\" where K is a closed convex matrix set and C = {X : sigma(X) in S} is defined by a convex constraint S on the ordered singular values. Using the classical spectral transfer identity, projection onto C reduces to an SVD plus a small quadratic program. For seven natural polyhedral S we embed this projector in a plain alternating projection (AP) loop. We experiment with two concrete families of K - linear constraints (an affine subspace intersected with an entrywise box) and ellipsoidal constraints (a non-centered anisotropic Frobenius ellipsoid) - although the method applies equally to more general convex constraints. The experiments expose three regimes: rapid feasibility, slow tail convergence, or informative infeasibility plateaus.","short_abstract":"We study matrix feasibility problems \"find X in K intersect C\" where K is a closed convex matrix set and C = {X : sigma(X) in S} is defined by a convex constraint S on the ordered singular values. Using the classical spectral transfer identity, projection onto C reduces to an SVD plus a small quadratic program. For sev...","url_abs":"https://arxiv.org/abs/2607.09254","url_pdf":"https://arxiv.org/pdf/2607.09254v1","authors":"[\"Shravan Mohan\"]","published":"2026-07-10T10:09:00Z","proceeding":"math.OC","tasks":"[\"math.OC\"]","methods":"[]","has_code":false}