TY - JOUR
T1 - Existence Results for Noncoercive Mixed Variational Inequalities in Finite Dimensional Spaces
AU - Iusem, Alfredo
AU - Lara, Felipe
N1 - Publisher Copyright:
© 2019, Springer Science+Business Media, LLC, part of Springer Nature.
PY - 2019/10/15
Y1 - 2019/10/15
N2 - We use asymptotic analysis and generalized asymptotic functions for studying nonlinear and noncoercive mixed variational inequalities in finite dimensional spaces in the nonconvex case, that is, when the operator is nonlinear and noncoercive and the function is nonconvex and noncoercive. We provide general necessary and sufficient optimality conditions for the set of solutions to be nonempty and compact. As a consequence, a characterization of the nonemptiness and compactness of the solution set, when the operator is affine and the function is convex, is given. Finally, a comparison with existence results for equilibrium problems is presented.
AB - We use asymptotic analysis and generalized asymptotic functions for studying nonlinear and noncoercive mixed variational inequalities in finite dimensional spaces in the nonconvex case, that is, when the operator is nonlinear and noncoercive and the function is nonconvex and noncoercive. We provide general necessary and sufficient optimality conditions for the set of solutions to be nonempty and compact. As a consequence, a characterization of the nonemptiness and compactness of the solution set, when the operator is affine and the function is convex, is given. Finally, a comparison with existence results for equilibrium problems is presented.
KW - Asymptotic analysis
KW - Asymptotic functions
KW - Equilibrium problems
KW - Noncoercive optimization
KW - Variational inequalities
UR - https://www.scopus.com/pages/publications/85067979847
U2 - 10.1007/s10957-019-01548-1
DO - 10.1007/s10957-019-01548-1
M3 - Article
AN - SCOPUS:85067979847
SN - 0022-3239
VL - 183
SP - 122
EP - 138
JO - Journal of Optimization Theory and Applications
JF - Journal of Optimization Theory and Applications
IS - 1
ER -