On perturbed steepest descent methods with inexact line search for bilevel convex optimization
On perturbed steepest descent methods with inexact line search for bilevel convex optimization
复制标题
双层凸优化的不精确线搜索扰动最速下降法
DOI：
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发表时间：
2011
期刊：
影响因子：
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通讯作者：
Á. D. De Pierro
中科院分区：
文献类型：
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作者：
E. Neto;Á. D. De Pierro
我们使用在早期工作中引入的解决凸约束优化问题的一般框架来获得约束集定义为给定函数的最小化集的问题的算法。此外，该算法允许将目标函数分解为可以单独处理的其他凸函数的和。我们证明了一般算法收敛于目标函数的最优值集合上的一个选择的凸lipschitz -可微函数。当在凸约束上使用正交投影时，我们检索到一种类似cimino的算法，该算法收敛于加权最小二乘解集上的最优解。此外，我们还展示了我们的方法在压缩感知和逆问题中的重要应用。
We use a general framework for solving convex constrained optimization problems introduced in an earlier work to obtain algorithms for problems with a constraint set defined as the set of minimizers of a given function. Also, the algorithms allow the objective function to be decomposed as a sum of other convex functions that can be treated separately. We prove that the general algorithm converges to the optimum of the objective function over the set of minima of a convex Lipschitz-differentiable function chosen previously. When using orthogonal projections onto the convex constraints, we retrieve a Cimmino-like algorithm that converges to the optimum over the set of weighted least squares solutions. Furthermore, we show an important application of our approach to compressed sensing and inverse problems.