Convergence of alternating optimization

• DOI: 10.5555/964885.964886
• Publication Date: 2003-12-01
• Authors: James C. Bezdek; Richard J. Hathaway

Let f : Rs → R be a real-valued function, and let x = (x1,...,xs)T ∈ partitioned into t subsets of non-overlapping variables as (X1,...,Xt)T, with Xi Rpi for i 1,...,t, Σi=1tpi s. Alternating optimization (AO) is an iterative procedure minimizing f(x) f(X1, X2,..., Xt) jointly over all by alternating restricted minimizations the individual X1,...., Xt. has been (more or less) studied used in wide variety areas. Here self-contained general convergence theory presented that applicable to partitionings x. Under reasonable assumptions, AO approach shown locally, q-linearly convergent, also exhibit type global convergence.