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Generalized weak sharp minima in cone-constrained convex optimization with applications

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Abstract

In this paper, we consider convex optimization problems with cone constraints (CPC in short). We study generalized weak sharp minima properties for (CPC) in the Banach space and Hilbert space settings, respectively. Some criteria and characterizations for the solution set to be a set of generalized weak sharp minima for (CPC) are derived. As an application, we propose an algorithm for (CPC) in the Hilbert space setting. Convergence analysis of this algorithm is given.

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Authors and Affiliations

  1. College of Mathematical Sciences, Chongqing Normal University, Chongqing, 401331, China

    H. L. Luo & J. W. Peng

  2. School of Economics and Business Administration, Chongqing University, Chongqing, 400030, China

    X. X. Huang

Authors
  1. H. L. Luo
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  2. X. X. Huang
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  3. J. W. Peng
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Corresponding author

Correspondence to X. X. Huang.

Additional information

This work is supported by the National Science Foundation of China, a research grant from Chongqing University, the Doctoral Start-Up Research Grant from Chongqing Normal University (Grant No. 10XLB016), the Natural Science Foundation of Chongqing (Grant No. CSTC, 2009BB8240), Chongqing science and technology commission (Grant No. cstc2011jjA00003) and the Special Fund of Chongqing Key Laboratory (CSTC).

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Luo, H.L., Huang, X.X. & Peng, J.W. Generalized weak sharp minima in cone-constrained convex optimization with applications. Comput Optim Appl 53, 807–821 (2012). https://doi.org/10.1007/s10589-012-9457-z

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  • DOI: https://doi.org/10.1007/s10589-012-9457-z

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