| [1] Bouhamidi A, Jbilou K. Sylvester Tikhonov-regularization methods in image restoration, Journal of Computational and Applied Mathematics[J]. 2007, 206:86-98.[2] Bouhamidi A, Jbilou K and Raydan M. Convex constrained optimization for large-scale generalized Sylvester equations[J]. Computational Optimization and Applications, 2011, 48:233-253.[3] Bouhamidi A, Enkhbat R, Jbilou K. Conditional gradient Tikhonov method for a convex optimization problem in image restoration[J]. Journal of Computational and Applied Mathematics, 2014, 255:580-592.[4] Bouhamidi A, Jbilou K. A Kronecker approximation with a convex constrained optimization method for blind image restoration[J]. Optimization Letters, 2012, 6:1251-1264.[5] Kamm J, Nagy J G. Kronecker product approximations for restoration image with reflexive boundary conditions[J]. SIAM Journal on Matrix Analysis and Applications, 2004, 25:829-841.[6] 方保镕, 周继东, 李医民. 矩阵论[M]. 北京:清华大学出版社, 2014, 254-264.[7] Birgin E G, Mart?nez J M and Raydan M. Nonmonotone spectral projected gradient methods on convex sets[J]. SIAM Journal on Optimization, 2000, 10:1196-1211.[8] Escalante R, Raydan M. Dykstra's algorithm for constrained least-squares rectangular matrix problems[J]. Computers Mathematics with Applications, 1998, 6:73-79.[9] Li J F, Hu X Y, Zhang L. Dykstra's algorithm for constrained least-squares doubly symmetric matrix problems[J]. Theoretical Computer Science, 2010, 411:2818-2826.[10] 李姣芬, 胡锡炎, 张磊. 闭凸集约束下线性矩阵方程求解的松弛交替投影算法[J]. 数学学报, 2014, 57:17-34.[11] Frank M, Wolfe P. An algorithm for quadratic programming[J]. Naval Research Logistics Quarterly, 1956, 3:95-110.[12] Weintraub A, Ortiz C, Gonz lez J. Accelerating convergence of the Frank-Wolfe algorithm[J]. Transportation Research Part B, 1985, 19:113-122.[13] Fukushima M. A modified Frank-Wolfe algorithm for solving the traffic assignment problem[J]. Transportation Research Part B, 1984, 18:169-177.[14] Arrache S, Ouafi R. Accelerating Convergence of the Frank-Wolfe Algorithm for Solving the Traffic Assignment Problem[J]. International Journal of Computer Science and Network Security, 2008, 8:181-186.[15] Wong K H, Teo K L. A conditional gradient method for a class of time-lag optimal control problems. Australian Mathematical Society. Journal. Series B. Applied Mathematics, 1984, 25:518-537.[16] Dunn J C. Diagonally modified conditional gradient methods for input constrained optimal control problems[J]. SIAM journal on control and optimization, 1986, 24:1177-1191.[17] Luss R, Teboulle M. Conditional gradient algorithmsfor rank-one matrix approximations with a sparsity constraint[J]. SIAM Review, 2013, 55:65-98.[18] Beck A, Teboulle M. A conditional gradient method with linear rate of convergence for solving convex linear systems[J]. Mathematical Methods of Operations Research, 2004, 59:235-247.[19] Chernov A V. On the convergence of the conditional gradient method as applied to the optimization of an elliptic equation[J]. Computational Mathematics and Mathematical Physics, 2015, 55:212-226.[20] Nocedal J, Wright S J. Numerical Optimization-Second Edtion, Springer, 2006. |
‖L（X：A1，…，At；B1，…，Bt）T‖2，其中‖.‖为Frobenius范数，L（X：A1，…，At；B1，…，Bt）为关于X的线性矩阵算子（或齐次线性变换），Ai∈Rp×m，Bj∈Rn×q i，j=1，…，n为算子L的系数矩阵，T为右端矩阵，Ω⊂Rm×n为界约束凸集合.提出了求解问题的条件梯度迭代算法及其简要收敛性分析，并给出条件梯度算法的几类加速形式.随机数据和图像恢复模型数据的实验结果表明说明算法是可行高效的. 