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

Gabriela Kováčová () and Firdevs Ulus ()
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Gabriela Kováčová: University of California
Firdevs Ulus: Bilkent University

Journal of Global Optimization, 2024, vol. 89, issue 4, No 6, 975-994

Abstract: Abstract It is possible to solve unbounded convex vector optimization problems (CVOPs) in two phases: (1) computing or approximating the recession cone of the upper image and (2) solving the equivalent bounded CVOP where the ordering cone is extended based on the first phase. In this paper, we consider unbounded CVOPs and propose an alternative solution methodology to compute or approximate the recession cone of the upper image. In particular, we relate the dual of the recession cone with the Lagrange dual of weighted sum scalarization problems whenever the dual problem can be written explicitly. Computing this set requires solving a convex (or polyhedral) projection problem. We show that this methodology can be applied to semidefinite, quadratic, and linear vector optimization problems and provide some numerical examples.

Keywords: Convex vector optimization; Linear vector optimization; Unbounded vector optimization; Recession cone; Convex projection; 90B50; 90C29; 90C25; 90C05; 90C20; 90C22 (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s10898-023-01351-3

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