有约束条件优化问题的MM算法

发布时间：2018-04-29 09:15

本文选题：MM算法 + Lasso　；参考：《兰州大学》2017年硕士论文

【摘要】：统计中诸多问题都可以转化为带约束条件的优化问题,然而这些优化函数往往因形式复杂或者不可导而很难求其最优值,如Lasso,Fused-Lasso,FLSA等.本文以MM(Majorization Minorization)算法为基础,具体研究了Lasso,Fused-Lasso,FLSA等具有约束条件的有化问题.首先,我们论证了用MM算法求解Lasso的过程实际上是在用变参数岭回归来逼近Lasso,而且在稀疏数据下速度很快.其次,本文给出了其他较为简单的约束优化问题的MM算法迭代式.再次,用MM算法求解Fused-Lasso问题时提出了合并记录算法和记录跳跃算法,以解决运算中出现分母为0的问题,并通过实践表明了合并记录法的效果.最后,文章又以MM算法为基础,用记录跳跃法来解决二维Fused-Lasso,并做了图像平滑的实例验证.
[Abstract]:Many problems in statistics can be transformed into optimization problems with constraints. However, these optimization functions are often difficult to find the optimal value due to the complexity of the form or non-derivation, such as Lasso-Fused-Lasso-FLSA and so on. In this paper, based on the MM(Majorization Minorization algorithm, we study the problem of LassoFused-Lasso-FLSA with constraint conditions. First of all, we demonstrate that the process of solving Lasso by MM algorithm is actually approaching Lassoby variable parameter ridge regression, and the speed is very fast under sparse data. Secondly, this paper gives the iterative formula of MM algorithm for other simple constrained optimization problems. Thirdly, when the MM algorithm is used to solve the Fused-Lasso problem, the merging record algorithm and the record jumping algorithm are proposed to solve the problem of denominator zero in the operation, and the effect of the combined recording method is proved by practice. Finally, based on MM algorithm, this paper uses the record jump method to solve the two-dimensional Fused-Lasso. and an example of image smoothing is given.
【学位授予单位】：兰州大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：F224

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