On strong and weak second-order necessary optimality conditions for nonlinear programming. (1st September 2016)

• Record Type: Journal Article
• Authors: Minchenko, L.; Leschov, A.
• Is Part Of: Optimization. Volume 65:Number 9(2016)
• Page Start: 1693
• Page End: 1702
• Publication Date: 2016-09-01
• Subjects: Nonlinear programming -- necessary optimality conditions -- constraint qualifications; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2016.1179300
• Languages: English
• ISSNs: 0233-1934

Abstract

Abstract: Second-order necessary optimality conditions play an important role in optimization theory. This is explained by the fact that most numerical optimization algorithms reduce to finding stationary points satisfying first-order necessary optimality conditions. As a rule, optimization problems, especially the high dimensional ones, have a lot of stationary points so one has to use second-order necessary optimality conditions to exclude nonoptimal points. These conditions are closely related to second-order constraint qualifications, which guarantee the validity of second-order necessary optimality conditions. In this paper, strong and weak second-order necessary optimality conditions are considered and their validity proved under so-called critical regularity condition at local minimizers.