Treffer: Approximating Solution for Posynomial Geometric Programming Problems using Interval Valued Function.

Geometric programming involving posynomials presents significant complexity when the coefficients are not represented as a single constant instead vary within a specific range. Numerous techniques have been followed to obtain the optimal solution to these kinds of problems. This paper focuses on PGPP’s having single objective function in the case when interval coefficients not only occur in the objective function but also on both the sides of the constraints. To achieve the optimality of the solution, interval coefficients are converted to a single representative value by employing interval-valued function thus reducing them to standard nonlinear programming problem. Afterwards, Karush-Kuhn-Tucker conditions and Taylor’s series expansion for multivariable taken upto first order leads us to derive the optimal solution. The function codes have been implemented in Python and performed using Google Colab. [ABSTRACT FROM AUTHOR]

المقال يناقش تقريب الحلول لمشاكل البرمجة الهندسية متعددة الحدود (PGPP) باستخدام الدوال ذات القيم الفترية. يتناول تعقيد البرمجة الهندسية عندما تتغير المعاملات ضمن نطاقات محددة بدلاً من أن تكون ثوابت ثابتة. يقترح المؤلفون خوارزمية تحول المعاملات الفترية إلى قيم تمثيلية فردية، مما يسمح بإعادة صياغة المشكلة كمسألة برمجة غير خطية قياسية. يتم اشتقاق الحلول المثلى باستخدام شروط كاروش-كون-تاكر وتوسيع سلسلة تايلور، مع تنفيذ عملي يتم توضيحه من خلال كود بايثون المنفذ على Google Colab. يتضمن البحث أمثلة عددية لتوضيح فعالية الطرق المقترحة. [Extracted from the article]

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