Author

Yuyuan Ouyang

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Preprint Sep 2026

A Compact Counterexample to Su\'arez's Berezin Approximation Question

Let $A^2(\mathbb D)$ be the unweighted Bergman space and write $Q_m(S)=T_{B_m(S)}$ for the map induced by the $m$th higher-order Berezin transform. Su\'arez asked in 2005 whether $Q_m(S)$ converges to $S$ in operator norm for every $S$ in the full Bergman Toeplitz algebra. We answer this question negatively in a strong...

Mishko Mitkovski, Yu-Yuan Ouyang · 0 citations

Preprint Sep 2026

An $O(1/T^3)$ algorithm for minimizing convex quadratic functions over the $L_1$ ball

We study convex quadratic minimization over the unit $L_1$ ball in which the maximum eigenvalue of the Hessian matrix is bounded by a positive constant $L$. We propose a novel first-order algorithm with objective value error bounded by $O(L/T^3)$ after $T$ gradient evaluations, assuming that the subproblems involved in...

Yu-Yuan Ouyang · 2 citations

Preprint Aug 2026

Quadratic Convexification of a Square Truncated by a Hyperbola

We study the quadratic convexification of the compact nonconvex set ${G} := \left[1/2,2\right]^2 \cap \{(x_1,x_2)\in\mathbb R^2\mid x_1x_2\leq1\}, $ which is a square truncated by a hyperbolic arc. Although the ordinary convex hull of ${G}$ is a triangle, its lifted convex hull in the complete quadratic space retains t...

Yipeng Zhang, Yuyuan Ouyang, Boshi Yang · 0 citations