Daun Li (Chinese University of Hong Kong)

Nonlinear Lagrangian theory in constrained nonlinear programming
Tuesday 13 June 2000 at 15.30, JCMB 6324

Abstract

The Lagrangian methods, the penalty function methods, and the successive quadratic programming method have been the most efficient solution algorithms in solving constrained optimization problems. In the convex situation, the existence of a saddle point guarantees the success of the dual search via sequential minimization of the Lagrangian function. In a presence of nonconvexity, however, the conventional dual search methods often fail to locate the global optimal solution of the primal problem. Recent research results by Li (1995), Goh and Yang (1997), Yang and Li (2000), and Sun and Li (1998, 2000) represent an extension from the traditional linear Lagrangian theory to nonlinear Lagrangian theory in an advancement to achieve a guarantee of the identification of an optimal solution of the primal problem via dual search. This talk summarizes recent progress in new dual formulations for constrained nonlinear programming with clear motivation and full geometric interpretation in order to better our understanding of the fundamental properties in constrained nonlinear programming problems and in the newly developed nonlinear Lagrangian duality theory. Prominent features in both the theoretical achievements and computational implementation of the new dual formulations will be addressed in this talk.

Seminars by year

Current 2019 2018 2017 2016 2015 2014 2013 2012 2011 2010 2009 2008 2007 2006 2005 2004 2003 2002 2001 2000 1999 1998 1997 1996