报告题目 (Title)：对称与非对称锥优化的数值方法
报告人 (Speaker)：戴彧虹 院士
报告时间 (Time)：2026年10月22日(周四) 14：00
报告地点 (Place)：校本部GJ303
邀请人(Inviter)：徐姿 教授
报告摘要：This talk presents recent advances in numerical methods for symmetric and nonsymmetric conic optimization. We first introduce a Newton augmented-Lagrangian method based on a smooth barrier augmented-Lagrangian formulation for symmetric cones. The method enjoys an $O(1/\varepsilon)$ global complexity bound and improves the conditioning of the associated Schur complement from $O(1/\mu^2)$ to $O(1/\mu)$. We then present a path-following smoothing Newton method for symmetric conic optimization. By revealing the self-concordant convex–concave structure underlying the reduced smooth barrier augmented-Lagrangian function, we establish an $O(\sqrt{\nu}\log(1/\varepsilon))$ iteration-complexity bound, matching that of short-step interior-point methods. Finally, we consider nonsymmetric conic optimization and develop an interior-point method with conjugate-free scaling. The scaling combines the primal barrier Hessian with a single-secant BFGS update and avoids derivatives of the conjugate barrier. The resulting method also achieves an $O(\sqrt{\nu}\log(1/\varepsilon))$ iteration-complexity bound. Numerical results on symmetric and nonsymmetric conic optimization problems illustrate the practical performance of the proposed approaches.