Second-Order Enhanced Optimality Conditions and Constraint Qualifications

Kuang Bai (), Yixia Song () and Jin Zhang ()
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Kuang Bai: The Hong Kong Polytechnic University
Yixia Song: Southern University of Science and Technology
Jin Zhang: Southern University of Science and Technology, Peng Cheng Laboratory

Journal of Optimization Theory and Applications, 2023, vol. 198, issue 3, No 15, 1264-1284

Abstract: Abstract In this paper, we study second-order necessary optimality conditions for smooth nonlinear programming problems. Employing the second-order variational analysis and generalized differentiation, under the weak constant rank (WCR) condition, we derive an enhanced version of the classical weak second-order Fritz–John condition which contains some new information on multipliers. Based on this enhanced weak second-order Fritz–John condition, we introduce the weak second-order enhanced Karush–Kuhn–Tucker condition and propose some associated second-order constraint qualifications. Finally, using our new second-order constraint qualifications, we establish new sufficient conditions for the existence of a Hölder error bound condition.

Keywords: Hölder error bounds; Nonlinear Programming; Second-order constraint qualifications; Second-order optimality conditions; 49K99; 90C30 (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s10957-023-02276-3

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