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Second order optimality conditions for theL 1-minimization problem

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Abstract

In this paper we establish necessary and sufficient second order optimality conditions for theL 1-problem. The approach is based on optimality criteria in terms of a curved second directional derivative, discussed in [3]. Our conditions generalize conditions for theL 1-problem given in [6]. An example demonstrates the usefulness of our criteria.

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References

  1. Ben-Tal A, Zowe J (1982) A unified theory of first and second order conditions for extremum problems in topological vector spaces. Math Programming Study 19:39–76

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  2. Ben-Tal A, Zowe J (1982) Necessary and sufficient optimality conditions for a class of nonsmooth minimization problems. Math Programming 24:70–92

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  3. Ben-Tal A, Zowe J (In press) Directional derivatives in nonsmooth optimization. Journal of Optimization Theory and Applications

  4. Ljusternik LA, Sobolev VJ (1974) Elements of functional analysis. John Wiley, New York

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  5. Royden HL (1968) Real analysis. Macmillan, New York

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  6. Wolfe JM (1976) NonlinearL 1 approximation of smooth functions. Journal of Approximation Theory 17:166–176

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Authors and Affiliations

  1. Technion, Israel Institute of Technology, Haifa, Israel

    A. Ben-Tal

  2. University of Bayreuth, Bayreuth, West-Germany

    J. Zowe

Authors
  1. A. Ben-Tal
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  2. J. Zowe
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Additional information

Communicated by J. Stoer

This research was supported by NSF Grant No. ECS-8214081 and the Fund for Promotion of Research at the Technion, and

Deutsche Forschungsgemeinschaft.

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Ben-Tal, A., Zowe, J. Second order optimality conditions for theL 1-minimization problem. Appl Math Optim 13, 45–58 (1985). https://doi.org/10.1007/BF01442198

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  • DOI: https://doi.org/10.1007/BF01442198

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