Approximating convex bodies using multiple objective optimization

Abstract: The problem to compute a polyhedral outer and inner approximation of a convex body can be reformulated as a problem to solve approximately a convex multiple objective optimization problem. This extends a previous result showing that multiple objective linear programming is equivalent to compute a $V$-representation of the projection of an $H$-polyhedron. These results are also discussed with respect to duality, solution methods and error bounds.

optimization and control

Audience: researchers in the topic

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