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

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

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Article ID: iaor19992586
Country: Netherlands
Volume: 80
Issue: 3
Start Page Number: 283
End Page Number: 313
Publication Date: Feb 1998
Journal: Mathematical Programming
Authors: ,
Keywords: trust regions
Abstract:

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 funtions 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.

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