Using negative curvature in solving nonlinear programs |
| |
Authors: | Donald Goldfarb Cun Mu John Wright Chaoxu Zhou |
| |
Affiliation: | 1.Department of Industrial Engineering and Operations Research,Columbia University,New York City,USA;2.Department of Electrical Engineering,Columbia University,New York City,USA |
| |
Abstract: | Minimization methods that search along a curvilinear path composed of a non-ascent negative curvature direction in addition to the direction of steepest descent, dating back to the late 1970s, have been an effective approach to finding a stationary point of a function at which its Hessian is positive semidefinite. For constrained nonlinear programs arising from recent applications, the primary goal is to find a stationary point that satisfies the second-order necessary optimality conditions. Motivated by this, we generalize the approach of using negative curvature directions from unconstrained optimization to equality constrained problems and prove that our proposed negative curvature method is guaranteed to converge to a stationary point satisfying second-order necessary conditions. |
| |
Keywords: | |
本文献已被 SpringerLink 等数据库收录! |
|