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Solving Inverse optimization problems in linear programming: a geometric and algorithmic approach | ||
| Caspian Journal of Mathematical Sciences | ||
| دوره 14، شماره 1 - شماره پیاپی 27، 2025، صفحه 62-71 اصل مقاله (140.61 K) | ||
| نوع مقاله: Research Articles | ||
| شناسه دیجیتال (DOI): 10.22080/cjms.2024.28094.1729 | ||
| نویسنده | ||
| Zohreh Akbari* | ||
| Department of Applied Mathematics, University of Mazandaran, Babolsar, Iran | ||
| تاریخ دریافت: 03 آذر 1403، تاریخ پذیرش: 14 آذر 1403 | ||
| چکیده | ||
| This paper addresses the inverse optimization problem for linear programming, focusing on determining a cost vector that ensures a pre-specified solution is optimal. Two approaches are presented: (i) using the Karush-Kuhn-Tucker (KKT) conditions, and (ii) a geometric perspective leveraging first-order necessary conditions. The latter method results in a convex quadratic programming problem, solved efficiently using the gradient projection method. Numerical experiments, including a complex resource allocation problem, validate the proposed approach. This study extends the theory and application of inverse optimization across logistics, resource management, and supply chain optimization. | ||
| کلیدواژه‌ها | ||
| Inverse optimization؛ Linear programming؛ Gradient projection method | ||
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آمار تعداد مشاهده مقاله: 49 تعداد دریافت فایل اصل مقاله: 32 |
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