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It is possible to solve unbounded convex vector optimization problems (CVOPs)in two phases: (1) computing or approximating the recession cone of the upperimage and (2) solving the equivalent bounded CVOP where the ordering cone isextended based on the first phase (Wagner et al., 2023). In this paper, weconsider unbounded CVOPs and propose an alternative solution methodology tocompute or approximate the recession cone of the upper image. In particular, werelate the dual of the recession cone with the Lagrange dual of weighted sumscalarization problems whenever the dual problem can be written explicitly.Computing this set requires solving a convex (or polyhedral) projectionproblem. We show that this methodology can be applied to semidefinite,quadratic and linear vector optimization problems and provide some numericalexamples.

Computing the recession cone of a convex upper image via convex projection