A Fast Algorithm for Matrix-Variable Triconvex Optimization with Application to Blind Image Deblurring

Matrix-variable triconvex optimization is a significant generalization of vector-variable triconvex or biconvex optimization and has been found to have popular applications. To reduce computation time and storage requirements, this paper presents a matrix-form iterative method for quickly solving matrix-variable constrained triconvex optimization problems. The proposed method is based on a matrix-form alternating projection iteration scheme in the form of matrix state spaces, where an efficient line search strategy is adopted by exploiting the optimality conditions of the problem for a larger step length. Compared with the existing vector-form alternating projection gradient method, the proposed method reduces storage requirements and computational cost, and thus is more computationally efficient. Each sequence generated by the proposed method is guaranteed to be globally convergent to a partial optimum under mild conditions. Finally, the proposed method is effectively applied to blind image deblurring problems. Computed results show that the proposed algorithm is superior to related iterative algorithms in terms of computation time and solution quality.