Second-Order Enhanced Optimality Conditions and Constraint Qualifications

Bai，Kuang1; Song，Yixia2; Zhang，Jin3

2023-09-01

10.1007/s10957-023-02276-3

Journal of Optimization Theory and Applications   Impact Factor & Quartile

0022-3239

1573-2878

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.

Hölder error bounds Nonlinear Programming Second-order constraint qualifications Second-order optimality conditions

SCI

English

Corresponding

NSFC["12222106","12201531"] ; Hong Kong Research Grants Council[PolyU153036/22p] ; Shenzhen Science and Technology Program[RCYX20200714114700072] ; Guangdong Basic and Applied Basic Research Foundation[2022B1515020082]

Operations Research & Management Science ; Mathematics

Operations Research & Management Science ; Mathematics, Applied

WOS:001042768300001

SPRINGER/PLENUM PUBLISHERS

ENGINEERING

2-s2.0-85166966929

Scopus

1.Department of Applied Mathematics,The Hong Kong Polytechnic University,Hong Kong
2.Department of Mathematics,Southern University of Science and Technology,Shenzhen,China
3.Department of Mathematics,National Center for Applied Mathematics Shenzhen,Southern University of Science and Technology,Peng Cheng Laboratory,Shenzhen,518055,China

Bai，Kuang,Song，Yixia,Zhang，Jin. Second-Order Enhanced Optimality Conditions and Constraint Qualifications[J]. Journal of Optimization Theory and Applications,2023,198(3):1264-1284.

Bai，Kuang,Song，Yixia,&Zhang，Jin.(2023).Second-Order Enhanced Optimality Conditions and Constraint Qualifications.Journal of Optimization Theory and Applications,198(3),1264-1284.

Bai，Kuang,et al."Second-Order Enhanced Optimality Conditions and Constraint Qualifications".Journal of Optimization Theory and Applications 198.3(2023):1264-1284.