A sequential quadratic programming algorithm without a penalty function, a filter or a constraint qualification for inequality constrained optimization. (3rd June 2022)

• Record Type: Journal Article
• Authors: Jian, Jinbao; Tang, Chunming; Hu, Qingjie; Han, Daolan
• Is Part Of: Optimization. Volume 71:Number 6(2022)
• Page Start: 1603
• Page End: 1635
• Publication Date: 2022-06-03
• Subjects: Inequality constraints -- nonlinear programming -- sequential quadratic programming -- line search -- finite convergence; 90C55 -- 90C30 -- 65K05; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2020.1827406
• Languages: English
• ISSNs: 0233-1934

Abstract

Abstract : This paper discusses a kind of nonlinear inequality constrained optimization problems without any constraint qualification. A new sequential quadratic programming algorithm for such problems is proposed, whose important features are as follows: (i) a new relaxation technique for the linearized constraints of the quadratic programming subproblem is introduced, which guarantees that the subproblem is always consistent and generates a favourable search direction; (ii) a weaker positive-definiteness assumption on the quadratic coefficient matrices is presented; (iii) a slightly new line search is adopted, where neither a penalty function nor a filter is used; (iv) an associated acceptable termination rule is introduced; (v) the finite convergence of the algorithm is proved. Furthermore, the numerical results on a collection of CUTE test problems show that the proposed algorithm is promising.