Level bundle-like algorithms for convex optimization
Level bundle-like algorithms for convex optimization
复制标题
用于凸优化的水平束类算法
DOI：
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复制
发表时间：
2013
影响因子：
1.8
通讯作者：
W. Oliveira
中科院分区：
文献类型：
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作者：
Yunier Bello Cruz;W. Oliveira
针对凸集上的凸函数极小化问题，我们提出了两种受限记忆层束形算法。如果记忆被限制为目标函数的一次线性化，那么这两种算法都是投影次梯度法的变体。第一个算法是在希尔伯特空间中提出的，是一个概念性的算法。证明了它强收敛于最接近初始迭代的解。此外，算法生成的整个迭代序列包含在一个直径等于初始点到解集之间的距离的球中。第二种算法是一个可实现的版本。它尽可能地模仿概念上的概念，以便类似于收敛性质。通过对几个两阶段随机线性规划的数值计算，验证了该算法的有效性。
We propose two restricted memory level bundle-like algorithms for minimizing a convex function over a convex set. If the memory is restricted to one linearization of the objective function, then both algorithms are variations of the projected subgradient method. The first algorithm, proposed in Hilbert space, is a conceptual one. It is shown to be strongly convergent to the solution that lies closest to the initial iterate. Furthermore, the entire sequence of iterates generated by the algorithm is contained in a ball with diameter equal to the distance between the initial point and the solution set. The second algorithm is an implementable version. It mimics as much as possible the conceptual one in order to resemble convergence properties. The implementable algorithm is validated by numerical results on several two-stage stochastic linear programs.