Abstract
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.
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This material is based upon work supported by the National Science Foundation under Grants 0203270, 0619080, and 0620286.
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Hager, W.W., Mair, B.A. & Zhang, H. An affine-scaling interior-point CBB method for box-constrained optimization. Math. Program. 119, 1–32 (2009). https://doi.org/10.1007/s10107-007-0199-0
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DOI: https://doi.org/10.1007/s10107-007-0199-0
Keywords
- Interior-point
- Affine-scaling
- Cyclic Barzilai–Borwein methods
- CBB
- PET
- Image reconstruction
- Global convergence
- Local convergence