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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2412.12895 |
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Table of Contents:
- This paper introduces and studies the generalized optimization problem (for short, GOP) defined by the conic order relation on a local sphere. The existence of solution to this problem is studied by using image space analysis (for short, ISA), and a class of regular weak separation functions on the local sphere is established. Moreover, a Lagrangian-type sufficient optimality condition and a saddle-point-type necessary optimality condition for GOP is obtained by a second class of weak separation functions, which are based on the Gerstewitz function and the directional distance function. The problem is transformed into a solvable real-valued optimization problem using scalarization methods.