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| An Interval Projection-Based Approach for Solving Interval Optimization Problems |
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| KeyWord:Interval-valued function, interval projection, interval-valued optimization, variational inequality |
| Author Name | Affiliation | | Morteza Pakdaman | School of Remote Sensing and Geomatics Engineering, Nanjing University of Information Science \& Technology (NUIST), Nanjing 210044, China
Research Institute of Meteorological and Atmospheric Science (RIMAS), Climate Research Institute (CRI), Mashhad, Iran | | Abouzar Mehraban | School of Remote Sensing and Geomatics Engineering, Nanjing University of Information Science \& Technology (NUIST), Nanjing 210044, China
Research Institute of Meteorological and Atmospheric Science (RIMAS), Climate Research Institute (CRI), Mashhad, Iran
School of Atmospheric Physics, Nanjing University of Information Science \& Technology (NUIST), Nanjing 210044, China | | Seyed Mohsen Miri | Department of Applied Mathematics, Faculty of Mathematical Sciences, Ferdowsi University of Mashhad, P. O. Box 1159, Mashhad 91775, Iran | | Shaoqi Gong | School of Remote Sensing and Geomatics Engineering, Nanjing University of Information Science \& Technology (NUIST), Nanjing 210044, China | | Majid Habibi Nokhandan | School of Remote Sensing and Geomatics Engineering, Nanjing University of Information Science \& Technology (NUIST), Nanjing 210044, China
Research Institute of Meteorological and Atmospheric Science (RIMAS), Climate Research Institute (CRI), Mashhad, Iran |
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| Abstract: |
| This research offers an extensive formulation for the projection of interval-valued elements onto closed convex sets under various scenarios. The proposed projection framework establishes a mathematical foundation for tackling optimization problems where the objective function takes on interval values, representing uncertainty or imprecision in model parameters. Based on this formulation, new necessary optimality conditions are derived, providing theoretical insight into the structure of solutions for interval-valued optimization problems. Furthermore, a variational-like inequality is developed as an equivalent form of the optimization problem, offering a convenient analytical tool for both theoretical and numerical investigations. To efficiently solve the resulting variational-like inequality, a projected gradient algorithm is proposed and analyzed. The convergence properties and computational feasibility of the method are examined through several numerical experiments, which demonstrate the effectiveness, accuracy, and robustness of the approach. |
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