报告题目：Convex Composite Quadratic Programming: A Restricted Wolfe Dual and a Symmetric Gauss-Seidel Decomposition Theorem

报告时间：2022-07-20  14:30 - 16:00

报告人：孙德锋 教授  香港理工大学

ZOOMID：561 420 9883  密码：tmcc2022

报告入口：https://zoom.us/j/5614209883?pwd=RlZEUHBCaFVXWW1tWjFFeHg4N2U2dz09

Abstract: While the Lagrange dual of linear programming is standard, it is not the case for convex quadratic programming. This ambiguity is caused by the rank deficiency of the Hessian of the objective function. In this talk, we shall introduce a restricted Wolfe dual for convex composite quadratic programming to address this issue. This restricted Wolfe dual possesses many nice theoretical properties that resemble those of linear conic programming and allows one to design efficient dual based augmented Lagrangian methods with guaranteed convergence. Interestingly, our study on the restricted Wolfe dual has also led to the proof of a symmetric Gauss-Seidel decomposition theorem, which in turn plays a critical role in the successful design of efficient accelerated proximal gradient methods for least squares optimization problems and the alternating direction methods of multipliers for multi-block convex optimization problems.