The objective of this paper is to investigate multiobjective semiinfinite
programming problems with vanishing constraints (in
brief, MSIPVC). We firstly propose both the vector Lagrange dual
problems and the scalarized Lagrange dual problems for MSIPVC
and explore duality relations under convexity assumptions. Then,
the saddle point optimality conditions for MSIPVC are considered.
Some examples are also given to illuminate the main results.