A Splitting Method for Orthogonality Constrained Problems

作者：Lai, Rongjie^*; Osher, Stanley

来源：Journal of Scientific Computing, 2014, 58(2): 431-449.

DOI：10.1007/s10915-013-9740-x

• Spherical constraint
• Orthogonality constraint
• Bregman iteration
• L1-harmonic energy minimization
• Conformal mapping

Orthogonality constrained problems are widely used in science and engineering. However, it is challenging to solve these problems efficiently due to the non-convex constraints. In this paper, a splitting method based on Bregman iteration is represented to tackle the optimization problems with orthogonality constraints. With the proposed method, the constrained problems can be iteratively solved by computing the corresponding unconstrained problems and orthogonality constrained quadratic problems with analytic solutions. As applications, we demonstrate the robustness of our method in several problems including direction fields correction, noisy color image restoration and global conformal mapping for genus-0 surfaces construction. Numerical comparisons with existing methods are also conducted to illustrate the efficiency of our algorithms.

• 出版日期2014-2