A derivative-free trust-region algorithm for composite nonsmooth optimization

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• 作者：Geovani Nunes Grapiglia ; Jinyun Yuan…
• 刊名：Computational and Applied Mathematics
• 出版年：2016
• 出版时间：July 2016
• 年：2016
• 卷：35
• 期：2
• 页码：475-499
• 全文大小：1,128 KB
• 刊物主题：Applications of Mathematics; Computational Mathematics and Numerical Analysis; Mathematical Applications in the Physical Sciences; Mathematical Applications in Computer Science;
• 出版者：Springer Basel
• ISSN：1807-0302
• 卷排序：35

文摘

The derivative-free trust-region algorithm proposed by Conn et al. (SIAM J Optim 20:387–415, 2009) is adapted to the problem of minimizing a composite function \(\varPhi (x)=f(x)+h(c(x))\), where \(f\) and \(c\) are smooth, and \(h\) is convex but may be nonsmooth. Under certain conditions, global convergence and a function-evaluation complexity bound are proved. The complexity result is specialized to the case when the derivative-free algorithm is applied to solve equality-constrained problems. Preliminary numerical results with minimax problems are also reported.KeywordsNonsmooth optimizationNonlinear programmingTrust-region methodsDerivative-free optimizationGlobal convergenceWorst-case complexity