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On second-order weak sharp minima of general nonconvex set-constrained optimization problems

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Listed:
  • Xiaoxiao Ma

    (University of Victoria)

  • Wei Ouyang

    (Yunnan Normal University
    Yunnan Key Laboratory of Modern Analytical Mathematics and Applications)

  • Jane J. Ye

    (University of Victoria)

  • Binbin Zhang

    (Kunming University of Science and Technology)

Abstract

This paper explores local second-order weak sharp minima for a broad class of nonconvex optimization problems. We propose novel second-order optimality conditions formulated through the use of classical and lower generalized support functions. These results are based on asymptotic second-order tangent cones and outer second-order tangent sets. Specifically, our findings eliminate the necessity of assuming convexity in the constraint set and/or the outer second-order tangent set, or the nonemptiness of the outer second-order tangent set. Furthermore, unlike traditional approaches, our sufficient conditions do not rely on strong assumptions such as the uniform second-order regularity of the constraint set and the property of uniform approximation of the critical cones.

Suggested Citation

  • Xiaoxiao Ma & Wei Ouyang & Jane J. Ye & Binbin Zhang, 2025. "On second-order weak sharp minima of general nonconvex set-constrained optimization problems," Journal of Optimization Theory and Applications, Springer, vol. 207(2), pages 1-24, November.
    • Handle: RePEc:spr:joptap:v:207:y:2025:i:2:d:10.1007_s10957-025-02775-5
    DOI: 10.1007/s10957-025-02775-5
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