Linearly constrained separable convex minimization problems have been raised widely in many real-world applications.In this paper,we propose a homotopy-based alternating direction method of multipliers for solving thi...Linearly constrained separable convex minimization problems have been raised widely in many real-world applications.In this paper,we propose a homotopy-based alternating direction method of multipliers for solving this kind of problems.The proposed method owns some advantages of the classical proximal alternating direction method of multipliers and homotopy method.Under some suitable condi-tions,we prove global convergence and the worst-case O(k/1)convergence rate in a nonergodic sense.Preliminary numerical results indicate effectiveness and efficiency of the proposed method compared with some state-of-the-art methods.展开更多
Separable multi-block convex optimization problem appears in many mathematical and engineering fields.In the first part of this paper,we propose an inertial proximal ADMM to solve a linearly constrained separable mult...Separable multi-block convex optimization problem appears in many mathematical and engineering fields.In the first part of this paper,we propose an inertial proximal ADMM to solve a linearly constrained separable multi-block convex optimization problem,and we show that the proposed inertial proximal ADMM has global convergence under mild assumptions on the regularization matrices.Affine phase retrieval arises in holography,data separation and phaseless sampling,and it is also considered as a nonhomogeneous version of phase retrieval,which has received considerable attention in recent years.Inspired by convex relaxation of vector sparsity and matrix rank in compressive sensing and by phase lifting in phase retrieval,in the second part of this paper,we introduce a compressive affine phase retrieval via lifting approach to connect affine phase retrieval with multi-block convex optimization,and then based on the proposed inertial proximal ADMM for 3-block convex optimization,we propose an algorithm to recover sparse real signals from their(noisy)affine quadratic measurements.Our numerical simulations show that the proposed algorithm has satisfactory performance for affine phase retrieval of sparse real signals.展开更多
The alternating direction method of multipliers （ADMM for short） is efficient for linearly constrained convex optimization problem. The practicM computationM cost of ADMM depends on the sub-problem solvers. The prox...The alternating direction method of multipliers （ADMM for short） is efficient for linearly constrained convex optimization problem. The practicM computationM cost of ADMM depends on the sub-problem solvers. The proximal point algorithm is a common sub-problem-solver. However, the proximal parameter is sensitive in the proximM ADMM. In this paper, we propose a homotopy-based proximal linearized ADMM, in which a homotopy method is used to soNe the sub-problems at each iteration. Under some suitable conditions, the global convergence and the convergence rate of O（1/k） in the worst case of the proposed method are proven. Some preliminary numerical results indicate the validity of the proposed method.展开更多
基金the National Natural Science Foundation of China(Nos.11571074 and 61672005)the Natural Science Foundation of Fujian Province(No.2015J01010).
文摘Linearly constrained separable convex minimization problems have been raised widely in many real-world applications.In this paper,we propose a homotopy-based alternating direction method of multipliers for solving this kind of problems.The proposed method owns some advantages of the classical proximal alternating direction method of multipliers and homotopy method.Under some suitable condi-tions,we prove global convergence and the worst-case O(k/1)convergence rate in a nonergodic sense.Preliminary numerical results indicate effectiveness and efficiency of the proposed method compared with some state-of-the-art methods.
基金Supported by the Natural Science Foundation of China(Grant Nos.12271050,12201268)CAEP Foundation(Grant No.CX20200027)+2 种基金Key Laboratory of Computational Physics Foundation(Grant No.6142A05210502)Science and Technology Program of Gansu Province of China(Grant No.21JR7RA511)the National Science Foundation(DMS 1816313)。
文摘Separable multi-block convex optimization problem appears in many mathematical and engineering fields.In the first part of this paper,we propose an inertial proximal ADMM to solve a linearly constrained separable multi-block convex optimization problem,and we show that the proposed inertial proximal ADMM has global convergence under mild assumptions on the regularization matrices.Affine phase retrieval arises in holography,data separation and phaseless sampling,and it is also considered as a nonhomogeneous version of phase retrieval,which has received considerable attention in recent years.Inspired by convex relaxation of vector sparsity and matrix rank in compressive sensing and by phase lifting in phase retrieval,in the second part of this paper,we introduce a compressive affine phase retrieval via lifting approach to connect affine phase retrieval with multi-block convex optimization,and then based on the proposed inertial proximal ADMM for 3-block convex optimization,we propose an algorithm to recover sparse real signals from their(noisy)affine quadratic measurements.Our numerical simulations show that the proposed algorithm has satisfactory performance for affine phase retrieval of sparse real signals.
基金supported by the National Natural Science Foundation of China(11571074,61170308)the Natural Science Foundation of Fujian Province(2015J01010)the Major Science Foundation of Fujian Provincial Department of Education(JA14037)
文摘The alternating direction method of multipliers （ADMM for short） is efficient for linearly constrained convex optimization problem. The practicM computationM cost of ADMM depends on the sub-problem solvers. The proximal point algorithm is a common sub-problem-solver. However, the proximal parameter is sensitive in the proximM ADMM. In this paper, we propose a homotopy-based proximal linearized ADMM, in which a homotopy method is used to soNe the sub-problems at each iteration. Under some suitable conditions, the global convergence and the convergence rate of O（1/k） in the worst case of the proposed method are proven. Some preliminary numerical results indicate the validity of the proposed method.
