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

Authors:
William W. Hager;Bernard A. Mair;Hongchao Zhang
Affiliations:
University of Florida, Department of Mathematics, PO Box 118105, 32611-8105, Gainesville, FL, USA;University of Florida, Department of Mathematics, PO Box 118105, 32611-8105, Gainesville, FL, USA;University of Minnesota, Institute for Mathematics and its Applications (IMA), 400 Lind Hall, 207 Church Street S.E., 55455-0436, Minneapolis, MN, USA
Venue:
Mathematical Programming: Series A and B
Year:
2009

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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.