In this paper, we analyze a class of methods for minimizing a proper lower semicontinuous extended-valued convex function . Instead of the original objective function f , we employ a convex approximation f k + 1 at the k th iteration. Some global convergence rate estimates are obtained. We illustrate our approach by proposing (i) a new family of proximal point algorithms which possesses the global convergence rate estimate even it the iteration points are calculated approximately, where are the proximal parameters, and (ii) a variant proximal bundle method. Applications to stochastic programs are discussed.
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机译:在本文中,我们分析了一类用于最小化适当的下半连续延伸值凸起功能的方法。而不是原始的物镜函数f,我们在k迭代采用凸近似f k + 1。获得了一些全局收敛率估算。我们通过提出(i)一种新的近端点算法来说明我们的方法,该近端点算法甚至估计估计迭代点,即大约是迭代点,在其中近侧参数,(ii)variant近端束法。讨论了对随机计划的应用。
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