Mathematical Programming

, Volume 119, Issue 1, pp 1–32 | Cite as

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

  • William W. Hager
  • Bernard A. Mair
  • Hongchao Zhang


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.


Interior-point Affine-scaling Cyclic Barzilai–Borwein methods CBB PET Image reconstruction Global convergence Local convergence 

Mathematics Subject Classfication (2000)

90C06 90C26 65Y20 


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Copyright information

© Springer-Verlag 2007

Authors and Affiliations

  • William W. Hager
    • 1
  • Bernard A. Mair
    • 1
  • Hongchao Zhang
    • 2
  1. 1.Department of MathematicsUniversity of FloridaGainesvilleUSA
  2. 2.Institute for Mathematics and its Applications (IMA)University of MinnesotaMinneapolisUSA

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