An affine scaling method for optimization problems with polyhedral constraints

William Hager () and Hongchao Zhang ()

Computational Optimization and Applications, 2014, vol. 59, issue 1, 163-183

Abstract: Recently an affine scaling, interior point algorithm ASL was developed for box constrained optimization problems with a single linear constraint (Gonzalez-Lima et al., SIAM J. Optim. 21:361–390, 2011 ). This note extends the algorithm to handle more general polyhedral constraints. With a line search, the resulting algorithm ASP maintains the global and R-linear convergence properties of ASL. In addition, it is shown that the unit step version of the algorithm (without line search) is locally R-linearly convergent at a nondegenerate local minimizer where the second-order sufficient optimality conditions hold. For a quadratic objective function, a sublinear convergence property is obtained without assuming either nondegeneracy or the second-order sufficient optimality conditions. Copyright Springer Science+Business Media New York 2014

Keywords: Interior point; Affine scaling; Cyclic Barzilai-Borwein methods; CBB; Global convergence; Local convergence; Polyhedral constraints; Box and linear constraints (search for similar items in EconPapers)
Date: 2014
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DOI: 10.1007/s10589-013-9535-x

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