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

Xiaoxiao Ma (), Wei Ouyang (), Jane J. Ye () and Binbin Zhang ()
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Xiaoxiao Ma: University of Victoria
Wei Ouyang: Yunnan Normal University
Jane J. Ye: University of Victoria
Binbin Zhang: Kunming University of Science and Technology

Journal of Optimization Theory and Applications, 2025, vol. 207, issue 2, No 2, 24 pages

Abstract: 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.

Keywords: Second-order weak sharp minima; Optimality condition; Support function; The lower generalized support function; Outer second-order tangent set; Asymptotic second-order tangent cone; 90C26; 90C46; 49J52; 49J53 (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s10957-025-02775-5

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