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A Partial First-Order Affine-Scaling Method

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Abstract

We present a partial first-order affine-scaling method for solving smooth optimization with linear inequality constraints. At each iteration, the algorithm considers a subset of the constraints to reduce the complexity. We prove the global convergence of the algorithm for general smooth objective functions, and show it converges at sublinear rate when the objective function is quadratic. Numerical experiments indicate that our algorithm is efficient.

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Authors and Affiliations

  1. Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100190, P. R. China

    Ran Gu & Ya Xiang Yuan

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  1. Ran Gu
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  2. Ya Xiang Yuan
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Correspondence to Ran Gu.

Additional information

This paper is partially supported by NSFC (Grant Nos. 11331012 and 11461161005)

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Gu, R., Yuan, Y.X. A Partial First-Order Affine-Scaling Method. Acta. Math. Sin.-English Ser. 35, 1–16 (2019). https://doi.org/10.1007/s10114-017-7097-z

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  • DOI: https://doi.org/10.1007/s10114-017-7097-z

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