A feasible directions method for nonsmooth convex optimization
A feasible directions method for nonsmooth convex optimization
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DOI：
10.1007/s00158-011-0634-y
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发表时间：
2011-09
影响因子：
3.9
通讯作者：
J. Herskovits;W. P. Freire;Mario Tanaka Fo;A. Canelas
中科院分区：
文献类型：
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作者：
J. Herskovits;W. P. Freire;Mario Tanaka Fo;A. Canelas
我们提出了一种新的技术，凸函数不一定光滑的最小化。我们的方法采用了一个等价的约束优化问题和近似的线性规划得到的切割平面。在每次迭代中，计算搜索方向和步长。如果步长被认为是“不严重的”，则添加切割平面并计算新的搜索方向。重复该过程，直到获得“严重”步骤。当这种情况发生时，搜索方向是约束等价问题的可行下降方向。为了计算搜索方向，我们采用与FDIPA中相同的公式，即用于约束优化的可行方向内点算法。我们证明了本方法的全局收敛性。描述了一组数值试验。该方法也成功地应用于鲁棒桁架的拓扑优化。我们的结果是与其他众所周知的既定方法所获得的。
We propose a new technique for minimization of convex functions not necessarily smooth. Our approach employs an equivalent constrained optimization problem and approximated linear programs obtained with cutting planes. At each iteration a search direction and a step length are computed. If the step length is considered “non serious”, a cutting plane is added and a new search direction is computed. This procedure is repeated until a “serious” step is obtained. When this happens, the search direction is a feasible descent direction of the constrained equivalent problem. To compute the search directions we employ the same formulation as in FDIPA, the Feasible Directions Interior Point Algorithm for constrained optimization. We prove global convergence of the present method. A set of numerical tests is described. The present technique was also successfully applied to the topology optimization of robust trusses. Our results are comparable to those obtained with other well known established methods.