Alternating Minimization, Proximal Minimization and Optimization Transfer Are Equivalent
Alternating Minimization, Proximal Minimization and Optimization Transfer Are Equivalent
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交替最小化、近似最小化和优化传递是等价的
DOI：
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发表时间：
2015
期刊：
影响因子：
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通讯作者：
Jong Soo Lee
中科院分区：
文献类型：
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作者：
C. Byrne;Jong Soo Lee
我们证明了近端最小化算法（PMA）、最大化最小化算法（MM）和交替最小化算法（AM）是等价的。每种算法都会导致目标函数的递减顺序。给出了PMA的新条件（目标函数递减序列的极限确实是目标函数的最小值），从而给出了序列Phi收敛于其最小值的新条件。然后将这些条件翻译成MM语言。给出了每种算法的示例，并提出了一些悬而未决的问题。
We show that proximal minimization algorithms (PMA), majorization minimization (MM), and alternating minimization (AM) are equivalent. Each type of algorithm leads to a decreasing sequence of objective function. New conditions on PMA are given (the limit of the decreasing sequence of objective function is indeed the infimum of the objective function), which lead to new conditions on AM for the sequence Phi to converge to its infimum. These conditions can then be translated into the language of MM. Examples are given of each type of algorithm and some open questions are posed.