Convergence of Alternating Optimization

By James C. Bezdek, Richard J. Hathaway. Neural Parallel Sci. Comput., 2003

519 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/c7a7b65446dcb4b6b58e5cfe67c11e9b22ec8602

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Citations in the corpus

Multi-Modal Bayesian Embeddings for Learning Social Knowledge Graphs (2015, methodology): “Similar to [ Bezdek and Hathaway, 2003 ] , we employ alternating optimization for inference.”
Towards Making Unlabeled Data Never Hurt (2011, methodology): “Examples include UniverSVM [15] which employs concaveconvex procedure (CCCP) [44], and meanS3VM [28] which employs alternating optimization [5].”
Constraining dense hand surface tracking with elasticity (2020, methodology): “We thus employ an alternating optimization method [Bezdek and Hathaway 2003] to solve the total optimization by first freezing the tetrahedral physics degrees of freedom and optimizing the remaining E vision + E link terms, and next freezing the vision-based surface degrees of freedom and…”
LOCAL CONVERGENCE OF ALTERNATING SCHEMES FOR OPTIMIZATION OF CONVEX PROBLEMS IN THE TT FORMAT (2011, methodology): “More generally, this type of method (more precisely its gradient version) is referred to as nonlinear block Gauss-Seidel, SOR or relaxation method [3, 29, 33].”
Generalized Dictionary for Multitask Learning with Boosting (2016, methodology): “2 can be optimized by the alternating optimization approach [Bezdek and Hathaway, 2003], as detailed in Algorithm 1.”
Federated Learning in Mobile Edge Networks: A Comprehensive Survey (2019, methodology): “Then, the MOCHA algorithm is proposed in which an alternating optimization approach [72] is used to approximately solve the minimization problem.”
Structured Graph Learning for Scalable Subspace Clustering: From Single View to Multiview (2021, unknown): “optimization [67], the objective function value of our problem (5) will monotonically decrease in each iteration.”
An Improved Multi-task Learning Approach with Applications in Medical Diagnosis (2008, methodology): “We use the results developed in the mathematical programming field [13,14] to obtain a global convergence analysis which requires that both subproblems, (5) and (6), have an unique optimal solution.”
On Local Convergence of Alternating Schemes for Optimization of Convex Problems in the Tensor Train Format (2013, methodology): “In fact, it locally equals the linear Gauss-Seidel iteration applied to the Hessian j′′(U∗) up to second order terms [3, 32, 33].”
Local Convergence of the Alternating Least Squares Algorithm for Canonical Tensor Approximation (2012, background): “There is a well-developed local theory for this type of method [1, 18, 23].”
Active learning via transductive experimental design (2006, methodology): “We propose an alternating optimization approach ( Bezdek & Hathaway, 2003 ) to problem (17) by repeating steps depicted in Algorithm 2, which is similar, in spirit, to the principle of Expectation-Maximization (EM) algorithms.”
SMILE: A Similarity-Based Approach for Multiple Instance Learning (2010, methodology): “The heuristic strategy is based on the alternating optimization method [21], [22].”