An affine-scaling interior-point CBB method for box-constrained optimization

• 成果类型: Article
• 署名作者: Hager, William W.; Mair, Bernard A.; Zhang, Hongchao
• 署名单位: State University System of Florida; University of Florida; University of Minnesota System; University of Minnesota Twin Cities
• 刊物名称: MATHEMATICAL PROGRAMMING
• ISSN/ISSBN: 0025-5610
• DOI: 10.1007/s10107-007-0199-0
• 发表日期: 2009
• 页码: 1-32
• 关键词: nonlinear minimization; newton methods; trust region; gradient; barzilai; algorithm

摘要

We develop an affine-scaling algorithm for box-constrained optimization which has the property that each iterate is a scaled cyclic Barzilai-Borwein (CBB) gradient iterate that lies in the interior of the feasible set. Global convergence is established for a nonmonotone line search, while there is local R-linear convergence at a nondegenerate local minimizer where the second-order sufficient optimality conditions are satisfied. Numerical experiments show that the convergence speed is insensitive to problem conditioning. The algorithm is particularly well suited for image restoration problems which arise in positron emission tomography where the cost function can be infinite on the boundary of the feasible set.