P000083
Variable Splitting Method For Matrix Optimization Problem With Symmetric Structure
*NACHUAN XIAO (State Key Laboratory of Scientific and Engineering Computing, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, and University of Chinese Academy of Sciences, China)
(XIN)
(YA-XIANG)
In this paper, we propose a variable splitting approach for a class of matrix optimization problems with orthogonal constraints and symmetric structure. Based on the symmetrically split variables in the original problems, we propose a simple smooth penalty model, where a quadratic penalty function is adopted to penalize the constraints introduced by our approach. We establish the equivalence between our model and the original problem under mild conditions and show that this approach can be extended to a wide range of matrix optimization problems. Based on the symmetrical characteristic of our model, we present an efficient alternating direction descent algorithm to solve our model. We prove the global convergence, local convergence rate and escaping saddle point property for our algorithm under loose conditions. Preliminary experiments illustrate the potential of our model.