joint work with Zhuoxuan Jiang, Chao Ding
We show that the quadratic assignment problem (QAP) is equivalent to the doubly nonnegative (DNN) problem with a rank constraint. A DC approach is developed to solve that DNN problem. And its subproblems are solved by the semi-proximal augmented Lagrangian method. The sequence generated by the proposed algorithm converges to a stationary point of the DC problem with a suitable parameter. Numerical results demonstrate: for some examples of QAPs, the optimal solutions can be found directly; for the others, good upper bounds with the feasible solutions are provided.
joint work with Liang Chen, Defeng Sun, Kim-Chuan Toh
In this talk, we show that for a class of linearly constrained convex composite optimization problems, an (inexact) symmetric Gauss-Seidel based majorized multi-block proximal alternating direction method of multipliers (ADMM) is equivalent to an inexact proximal augmented Lagrangian method (ALM). This equivalence not only provides new perspectives for understanding some ADMM-type algorithms but also supplies meaningful guidelines on implementing them to achieve better computational efficiency.
The nonsmooth composite matrix optimization problem, in particular, the matrix norm optimization problem, is a generalization of the matrix conic program with wide applications in numerical linear algebra, computational statistics and engineering. This talk is devoted to study some perturbation properties of matrix optimization problems