Convergence of alternating optimization Export

@article{bezdek03, abstract = {Let f : R s \&\#8594; R be a real-valued function, and let x = (x 1 ,...,x s ) T \&\#8712; R s be partitioned into t subsets of non-overlapping variables as x = (X 1 ,...,X t ) T , with X i \&\#8712; R p i for i = 1,...,t, \&\#931; i=1 t p i = s. Alternating optimization (AO) is an iterative procedure for minimizing f(x) = f(X 1 , X 2 ,..., X t ) jointly over all variables by alternating restricted minimizations over the individual subsets of variables X 1 ,...., X t . Alternating optimization has been (more or less) studied and used in a wide variety of areas. Here a self-contained and general convergence theory is presented that is applicable to all partitionings of x. Under reasonable assumptions, the general AO approach is shown to be locally, q-linearly convergent, and to also exhibit a type of global convergence.}, address = {Atlanta, GA, USA}, author = {Bezdek, James C. and Hathaway, Richard J.}, citeulike-article-id = {5035101}, citeulike-linkout-0 = {http://portal.acm.org/citation.cfm?id=964886}, issn = {1061-5369}, journal = {Neural, Parallel Sci. Comput.}, keywords = {bezdek03}, number = {4}, pages = {351--368}, posted-at = {2009-07-01 18:38:36}, priority = {4}, publisher = {Dynamic Publishers, Inc.}, title = {Convergence of alternating optimization}, url = {http://portal.acm.org/citation.cfm?id=964886}, volume = {11}, year = {2003} }

TY - JOUR ID - bezdek03 L3 - citeulike-article-id:5035101 N2 - Let f : R s → R be a real-valued function, and let x = (x 1 ,...,x s ) T ∈ R s be partitioned into t subsets of non-overlapping variables as x = (X 1 ,...,X t ) T , with X i ∈ R p i for i = 1,...,t, Σ i=1 t p i = s. Alternating optimization (AO) is an iterative procedure for minimizing f(x) = f(X 1 , X 2 ,..., X t ) jointly over all variables by alternating restricted minimizations over the individual subsets of variables X 1 ,...., X t . Alternating optimization has been (more or less) studied and used in a wide variety of areas. Here a self-contained and general convergence theory is presented that is applicable to all partitionings of x. Under reasonable assumptions, the general AO approach is shown to be locally, q-linearly convergent, and to also exhibit a type of global convergence. IS - 4 JF - Neural, Parallel Sci. Comput. SN - 1061-5369 AD - Atlanta, GA, USA EP - 368 TI - Convergence of alternating optimization PB - Dynamic Publishers, Inc. VL - 11 SP - 351 KW - bezdek03 AU - Bezdek, James AU - Hathaway, Richard PY - 2003/// UR - http://portal.acm.org/citation.cfm?id=964886 ER -