Paper Info
Title
The Theory of 2-Regularity for Mappings with Lipschitzian Derivatives and its Applications to Optimality Conditions
Abstract
We study local structure of a nonlinear mapping near points where standard regularity and/or smoothness assumptions need not be satisfied. We introduce a new concept of 2-regularity a certain kind of second-order regularity for a once differentiable mapping whose derivative is Lipschitz continuous. Under this 2-regularity condition, we obtain the representation theorem and the covering theorem i.e., stability with respect to “right-hand side” perturbations under assumptions that are weaker than those previously employed in the literature for results of this type. These results are further used to derive a constructive description of the tangent cone to a set defined by 2-regular equality constraints and optimality conditions for related optimization problems. The class of mappings introduced and studied in the paper appears to be a convenient tool for treating complementarity structures by means of an appropriate equation-based reformulation. Optimality conditions for mathematical programs with equivalently reformulated complementarity constraints are also discussed.
Year
DOI
Venue
2002
10.1287/moor.27.3.614.308
Math. Oper. Res.
Keywords
Field
DocType
optimality condition,standard regularity,optimality conditions,tangent cone,complementarity,covering,complementarity constraint,nonlinear mapping,representation theorem,c1,2-regularity condition,mathematical programs with equilibrium constraints,differentiable mapping,c,appropriate equation-based reformulation,second-order regularity,complementarity structure,2-regularity,1-mapping,lipschitzian deriatives
Discrete mathematics,Algebra,Mathematics,Derivative (finance)
Journal
Volume
Issue
ISSN
27
3
0364-765X
Citations 
PageRank 
References 
22
2.35
8
Authors
2
Name
Order
Citations
PageRank
A. F. Izmailov123821.76
M. V. Solodov260072.47