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

Author

Listed:
  • H. Luo
  • X. Huang
  • J. Peng

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. Copyright Springer Science+Business Media, LLC 2012

Suggested Citation

  • H. Luo & X. Huang & J. Peng, 2012. "Generalized weak sharp minima in cone-constrained convex optimization with applications," Computational Optimization and Applications, Springer, vol. 53(3), pages 807-821, December.
    • Handle: RePEc:spr:coopap:v:53:y:2012:i:3:p:807-821
    DOI: 10.1007/s10589-012-9457-z
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    References listed on IDEAS

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    1. X. X. Huang & X. Q. Yang & K. L. Teo, 2004. "Characterizing Nonemptiness and Compactness of the Solution Set of a Convex Vector Optimization Problem with Cone Constraints and Applications," Journal of Optimization Theory and Applications, Springer, vol. 123(2), pages 391-407, November.
    2. V. Jeyakumar & G. M. Lee & N. Dinh, 2004. "Lagrange Multiplier Conditions Characterizing the Optimal Solution Sets of Cone-Constrained Convex Programs," Journal of Optimization Theory and Applications, Springer, vol. 123(1), pages 83-103, October.
    3. Alexander Shapiro & Jie Sun, 2004. "Some Properties of the Augmented Lagrangian in Cone Constrained Optimization," Mathematics of Operations Research, INFORMS, vol. 29(3), pages 479-491, August.
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