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A variational principle for vector equilibrium problems. (English) Zbl 1019.49017
The author describes a variational principle for vector equilibrium problems of finding $x\in K$ such that $$f(x,y)\not\in -\text{int }P$$ for all $y\in K$, where $\text{ int}P$ denotes the topological interior of the cone $P$, $X$ is a real topological vector space, $K$ is a nonempty closed convex subset of $X$, $(Y,P)$ is a real ordered topological vector space, and $f:X\times X\to Y$ is a mapping with $f(x,x)=0$ for all $x\in X$. Under some conditions, the author analyses the solutions for vector equilibrium problems and obtains some new results.

49J40Variational methods including variational inequalities
90C29Multi-objective programming; goal programming
91B52Special types of equilibria in economics
Full Text: DOI
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