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Trust region affine scaling
algorithms for linearly constrained convex and concave programs

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R.D.C. Monteiro and Y. Wang

We study a trust region affine scaling algorithm for solving the linearly constrained convex or
concave programming problem. Under primal nondegeneracy assumption, we prove that every
accumulation point of the sequence generated by the algorithm satisfies the first order necessary
condition for optimality of the problem. For a special class of convex or concave functions satisfying
a certain invariance condition on their Hessians, it is shown that the sequences of iterates and
objective function values generated by the algorithm converge $R$-linearly and $Q$-linearly,
respectively. Moreover, under primal nondegeneracy and for this class of objective functions, it is
shown that the limit point of the sequence of iterates satisfies the first and second order necessary
conditions for optimality of the problem.