NDLI: On Using the Elastic Mode in Nonlinear Programming Approaches to Mathematical Programs with Complementarity Constraints

Content Provider	Society for Industrial and Applied Mathematics (SIAM)
Author	Anitescu, Mihai
Copyright Year	2005
Abstract	We investigate the possibility of solving mathematical programs with complementarity constraints (MPCCs) using algorithms and procedures of smooth nonlinear programming. Although MPCCs do not satisfy a constraint qualification, we establish sufficient conditions for their Lagrange multiplier set to be nonempty. MPCCs that have nonempty Lagrange multiplier sets and satisfy the quadratic growth condition can be approached by the elastic mode with a bounded penalty parameter. In this context, the elastic mode transforms MPCC into a nonlinear program with additional variables that has an isolated stationary point and local minimum at the solution of the original problem, which in turn makes it approachable by sequential quadratic programming (SQP) algorithms. One such algorithm is shown to achieve local linear convergence once the problem is relaxed. Under stronger conditions, we also prove superlinear convergence to the solution of an MPCC using an adaptive elastic mode approach for an SQP algorithm recently analyzed in an MPCC context in [R. Fletcher, S. Leyffer, S. Sholtes, and D. Ralph, Local Convergence of SQP Methods for Mathematical Programs with Equilibrium Constraints, Tech. report NA 210, University of Dundee, Dundee, UK, 2002]. Our assumptions are more general since we do not use a critical assumption from that reference. In addition, we show that the elastic parameter update rule will not interfere locally with the superlinear convergence once the penalty parameter is appropriately chosen.
Starting Page	1203
Ending Page	1236
Page Count	34
File Format	PDF
ISSN	10526234
DOI	10.1137/S1052623402401221
e-ISSN	10957189
Journal	SIAM Journal on Optimization (SJOPE8)
Issue Number	4
Volume Number	15
Language	English
Publisher	Society for Industrial and Applied Mathematics
Publisher Date	2006-07-28
Access Restriction	Subscribed
Subject Keyword	elastic mode Optimization and variational techniques nonlinear programming mathematical programs with complementarity constraints complementarity constraints Methods of successive quadratic programming type mathematical programs with equililbrium constraints Nonlinear programming Complementarity and equilibrium problems and variational inequalities sequential quadratic programming Methods of nonlinear programming type
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Theoretical Computer Science Software

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