On second-order optimality conditions in nonlinear optimization. (2nd January 2017)

• Record Type: Journal Article
• Authors: Andreani, Roberto; Behling, Roger; Haeser, Gabriel; Silva, Paulo J.S.
• Is Part Of: Optimization methods and software. Volume 32:Number 1(2017)
• Page Start: 22
• Page End: 38
• Publication Date: 2017-01-02
• Subjects: nonlinear optimization -- constraint qualifications -- second-order optimality conditions; 90C46 -- 90C30; Mathematical optimization -- Periodicals; Algorithms -- Periodicals; 519.7
• DOI: 10.1080/10556788.2016.1188926
• Languages: English
• ISSNs: 1055-6788

Abstract

Abstract : In this work we present new weak conditions that ensure the validity of necessary second-order optimality conditions (SOC) for nonlinear optimization. We are able to prove that weak and strong SOCs hold for all Lagrange multipliers using Abadie-type assumptions. We also prove weak and strong SOCs for at least one Lagrange multiplier imposing the Mangasarian–Fromovitz constraint qualification and a weak constant rank assumption.