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# روش آشفتگی هموتوپی برای مسائل برنامه نویسی خطی

عنوان انگلیسی
Homotopy perturbation method for linear programming problems
کد مقاله سال انتشار تعداد صفحات مقاله انگلیسی ترجمه فارسی
25481 2014 5 صفحه PDF 6 صفحه WORD
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منبع Publisher : Elsevier - Science Direct (الزویر - ساینس دایرکت)

Journal : Applied Mathematical Modelling, Volume 38, Issues 5–6, 1 March 2014, Pages 1607–1611

فهرست مطالب ترجمه فارسی
چکیده.
کلید واژه
1. مقدمه
2. روش آشفتگی هموتوپی (HPM) برای دستگاه های خطی
3. مثال نقض
4. کاربرد درستHPM  برای حل مسائل LP
5.نتیجه
ترجمه کلمات کلیدی
برنامه نویسی خطی، روش آشفتگی هموتوپی، دوگانگی ، شرطKKT
کلمات کلیدی انگلیسی
Linear programming, Homotopy perturbation method, Duality, KKT condition,
ترجمه چکیده
دراین مقاله، او روش آشفتگی هموتوپی (HPM) رابرای حل مسائل برنامه نویسی خطی(LP) بکارمیبرد. این مقاله نشان میدهد که برخی یافته های اخیردرباره این موضوع نمیتواند برای همه موارد بکاربرده شود. بنابراین، ما کاربرد درست ازHPM برای مسائلLP فراهم میکنیم. روش پیشنهادی یک ساختارساده ومناسب دارد. درنهایت، یک مثال عددی برای توضیح دادن روش پیشنهادی نمایش داده میشود.

#### چکیده انگلیسی

In this paper, He’s homotopy perturbation method (HPM) is applied for solving linear programming (LP) problems. This paper shows that some recent findings about this topic cannot be applied for all cases. Furthermore, we provide the correct application of HPM for LP problems. The proposed method has a simple and graceful structure. Finally, a numerical example is displayed to illustrate the proposed method.

#### مقدمه انگلیسی

Experiential surveys show that linear programming (LP) is one of the most important techniques in applied mathematics. Many real-world problems can be transformed to linear programming model. Hence this model is an indispensable tool in today’s applications such as energy, military, transportation, manufacturing, etc. There are many methods for solving LP (see  and references therein). Recently, Mehrabinezhad and Saberi-Nadjafi , presented a new method to solve LP based on the homotopy perturbation method (HPM). HPM was first proposed by He in 1998  and was further developed and improved by him (see, , , ,  and  and the references therein). He, presented a homotopy perturbation technique based on the introduction of homotopy in topology, coupled with the traditional perturbation method for the solution of algebraic equations. This technique provides a summation of an infinite series with easily computable terms, which converges rapidly to the solution of the problem. In the literature, various authors have successfully applied HPM for many kinds of different problems such as nonlinear partial differential equations  and , nonlinear integral and integro-differential equations ,  and , fractional IVPs , nonlinear systems  and also linear systems  and . For details of the number of publications on HPM according to web of science, we refer to [7, Fig. 1]. In this paper we study the homotopy perturbation method and point out some problems in the article . Furthermore, we use HPM for solving linear programming (LP) problems under unrestricted variables. This paper is organized as follows. In Section 2, we present some notations and a brief review of the homotopy perturbation model for solving linear system. In Section 3, we point out the problems of the mentioned paper. In Section 4, we introduce application of HPM for LP under unrestricted variables with some examples.

#### نتیجه گیری انگلیسی

In this paper, we have applied He’s homotopy perturbation method (HPM) for linear programming (LP) problems. We have shown that the model of  cannot be applied for all cases. Finally, a numerical example is displayed to illustrate the proposed method.

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