Image Space Analysis to the generalized optimization problem on a local sphere

2024/12/17 by Liwen Zhou, Min Tang, Zhou, Li-wen +5
Computer Science · Mathematics · #Computer science #FOS: Mathematics #Mathematical optimization #Mathematics #Medical Image Segmentation Techniques #Optimization and Control (math.OC) #Optimization problem #Space (punctuation)

paper · pdf · doi:10.48550/arxiv.2412.12895

openalex publication_date 2024/12/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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.

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