• Journal of applied mathematics & informatics
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• 제29권1_2호
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• pp.337-349
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• 2011

This paper is concerned with deriving necessary and sufficient optimality conditions for a fuzzy linear programming problem. Toward this end, an equivalence between fuzzy and crisp linear programming problems is established by means of a specific ranking function. Under this setting, a main theorem gives optimality conditions which do not seem to be in conflict with the so-called Karush-Kuhn-Tucker conditions for a crisp linear programming problem.

• KIEAE Journal
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• 제3권2호
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• pp.51-58
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• 2003

The purpose of this study is to present rational methods of multi-criteria optimization of the shape of energy saving buildings. The object is to determine the optimum dimension of the shape of a building, based on the following criteria: minimum building costs (including the cost of materials and construction) and yearly heating costs. Mathematical model described heat losses and gains in a building during the heating season. It takes into consideration heat losses through wall, roof, floor and windows. Particular attention was paid to have a more detailed description of heat gains due to solar radiation. On the assumption that shape of building is rectangle in order to solve the problem, the proportions of wall length and building height are determined by using non-linear programing methods(Kuhn-Tucker Conditions). The results constitute information for designers on the optimum proportions of wall lengths, height, and the ratios of window to wall areas for energy saving buildings.

• Journal of applied mathematics & informatics
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• 제29권5_6호
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• pp.1157-1165
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• 2011

The Karush-Kuhn-Tucker (KKT) necessary optimality conditions for nonlinear differentiable programming problems are also sufficient under suitable convexity assumptions. The KKT conditions in multiobjective programming problems with interval-valued objective and constraint functions are derived in this paper. The main contribution of this paper is to obtain the Pareto optimal solutions by resorting to the sufficient optimality condition.

• Journal of applied mathematics & informatics
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• 제17권1_2_3호
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• pp.433-455
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• 2005

Fritz John, and Karush-Kuhn-Tucker type optimality conditions for a constrained variational problem involving higher order derivatives are obtained. As an application of these Karush-Kuhn-Tucker type optimality conditions, Wolfe and Mond-Weir type duals are formulated, and various duality relationships between the primal problem and each of the duals are established under invexity and generalized invexity. It is also shown that our results can be viewed as dynamic generalizations of those of the mathematical programming already reported in the literature.

• 한국정보통신학회:학술대회논문집
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• 한국정보통신학회 2014년도 춘계학술대회
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• pp.89-93
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• 2014

제품 리뷰들은 잠재적인 고객의 구매 선택에 매우 중요하다. 제품 리뷰들은 또한 제조사들로 하여금 자신들의 제품의 문제점을 찾고 경쟁자들의 비즈니스 정보를 수집하는 데 사용된다. 그러나 어떤 사람들은 가짜 리뷰를 쓰고, 잠재적인 고객들과 제조사들로 하여금 잘못된 선택을 하게 만든다. 따라서 가짜 리뷰 판별은 전자 상거래 사이트에서 주된 문제들 중 하나이다. 서포트 벡터 머신즈(SVM)는 좋은 성능을 보이는 중요한 텍스트 분류 알고리즘이다. 본 논문에서는 온라인 리뷰 스팸을 판별하기 위해 가중치, Karush-Kuhn-Tucker(KKT) 조건의 확장, 그리고 컨벡스 헐(Convex Hull)에 근거한 점증적 알고리즘을 제시한다. 최종적으로 우리는 제시된 알고리즘의 성능을 이론적으로 분석한다.

• 대한기계학회논문집A
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• 제27권2호
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• pp.268-275
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• 2003

Generally, structural optimization is carried out based on external static loads. All forces have dynamic characteristics in the real world. Mathematical optimization with dynamic loads is extremely difficult in a large-scale problem due to the behaviors in the time domain. The dynamic loads are often transformed into static loads by dynamic factors, design codes, and etc. Therefore, the optimization results can give inaccurate solutions. Recently, a systematic transformation has been proposed as an engineering algorithm. Equivalent static loads are made to generate the same displacement field as the one from dynamic loads at each time step of dynamic analysis. Thus, many load cases are used as the multiple leading conditions which are not costly to include in modern structural optimization. In this research, it is mathematically proved that the solution of the algorithm satisfies the Karush-Kuhn-Tucker necessary condition. At first, the solution of the new algorithm is mathematically obtained. Using the termination criteria, it is proved that the solution satisfies the Karush-Kuhn-Tucker necessary condition of the original dynamic response optimization problem. The application of the algorithm is discussed.

• Journal of applied mathematics & informatics
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• 제27권1_2호
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• pp.123-137
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• 2009

A multiobjective variational problem involving higher order derivatives is considered and Fritz-John and Karush-Kuhn-Tucker type optimality conditions for this problem are derived. As an application of Karush-Kuhn-Tucker optimality conditions, Wolfe type dual to this variational problem is constructed and various duality results are validated under generalized invexity. Some special cases are mentioned and it is also pointed out that our results can be considered as a dynamic generalization of the already existing results in nonlinear programming.

• KIEAE Journal
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• 제3권2호
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• pp.17-24
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• 2003

The purpose of this study is to present rational methods of multi-criteria optimization of the envelope of buildings. The object is to determine the optimum R-value of the envelope of a building, based on the following criteria: minimum building costs (including the cost of materials and construction) and yearly heating costs. Mathematical model described heat losses and gains in a building during the heating season. It takes into consideration heat losses through wall, roof, floor and windows. Particular attention was paid to have a more detailed description of heat gains due to solar radiation. On the assumption that shape of building is rectangle in order to solve the problem, optimum R-value of the envelope of a building is determined by using non-linear programing methods(Kuhn-Tucker Conditions). The results constitute information for designers on the optimum R-value of a building envelope for energy saving buildings.

• Journal of Communications and Networks
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• 제18권4호
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• pp.629-638
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• 2016

In this paper, we investigate an energy-efficient resource allocation problem in a two-way relay (TWR) network consisting of multiple user pairs and an amplify-and-forward (AF) relay. As the users and relay have individual energy efficiencies (EE), we formulate a multi-objective optimization problem (MOOP). A single-objective optimization problem (SOOP) of the MOOP is introduced using a weighted-sum method, which achieves a single Pareto optimal point of the MOOP. To derive the algorithm for the SOOP, we propose a more tractable equivalent problem using the Karush-Kuhn-Tucker conditions of the SOOP, which guarantees convergence at the local optimal points. The proposed equivalent problem can be efficiently solved by the proposed iterative algorithm. Numerical results demonstrate the effectiveness of the proposed algorithm in achieving the optimal EE in multi-user AF TWR networks.

• Journal of applied mathematics & informatics
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• 제31권1_2호
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• pp.189-197
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• 2013

In this paper, Karush-Kuhn-Tucker type sufficient optimality conditions are obtained for a feasible point of a nonsmooth multiobjective fractional programming problem to be an efficient or properly efficient by using generalized ($F,{\rho},{\sigma}$)-type I functions.