## Communications in Mathematical Analysis

### Arcwise Connectedness of Efficient Sets

Ivan Ginchev

#### Abstract

Let $E$ be a topological vector space and $C$ a pointed closed convex cone. For a set $Q$ in $E$ we prove arcwise connectedness of the efficient point set $Max(Q|C)$ between any two points of a closed set $M \subset Max(Q|C)$ with a compact closed convex hull and having certain additional property. An application to a class of non-convex in general sets is given. The method generalizes the one from [6] concerning compact convex sets and allows also for such sets to obtain a more general result.

#### Article information

Source
Commun. Math. Anal., Volume 10, Number 2 (2011), 1-17.

Dates
First available in Project Euclid: 28 November 2011

https://projecteuclid.org/euclid.cma/1322489161

Mathematical Reviews number (MathSciNet)
MR2859848

Zentralblatt MATH identifier
1235.90137

Subjects
Primary: 90C29: Multi-objective and goal programming

#### Citation

Ginchev, Ivan. Arcwise Connectedness of Efficient Sets. Commun. Math. Anal. 10 (2011), no. 2, 1--17. https://projecteuclid.org/euclid.cma/1322489161

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