An affine scaling method for optimization problems with polyhedral constraints

Document Type

Article

Publication Date

1-1-2014

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. © 2013 Springer Science+Business Media New York.

Publication Source (Journal or Book title)

Computational Optimization and Applications

First Page

163

Last Page

183

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