• Journal of the Korea Society of Computer and Information
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• v.12 no.5
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• pp.121-129
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• 2007

Scalarization is a process that a parallel construct like an array statement of Fortran 90 or FORALL of HPF is converted into sequential loops that maintain the correct semantics. Most compilers of HPF, recognized as a standard data parallel language, convert a HPF program into a Fortran 77 program inserted message passing primitives. During scalariztion, a parallel construct FORALL should be translated into Fortran 77 DO loops maintaining the semantics of FORALL. In this paper, we propose a scalarization algorithm which converts a FORALL construct into a DO loop with improved performance. For this, we define and use a relation distance vector to keep necessary dependence informations. Then we evaluate execution times of the codes generated by our method and by PARADIGM compiler method for various array sizes.

• Bulletin of the Korean Mathematical Society
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• v.48 no.6
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• pp.1225-1233
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• 2011

In this paper, without assumption of monotonicity, we study the compactness and the connectedness of the weakly efficient solutions set to vector equilibrium problems by using scalarization method in locally convex spaces. Our results improve the corresponding results in [X. H. Gong, Connectedness of the solution sets and scalarization for vector equilibrium problems, J. Optim. Theory Appl. 133 (2007), 151-161].

• East Asian mathematical journal
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• v.26 no.3
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• pp.415-421
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• 2010

Many kinds of Minty's lemmas show that Minty-type variational inequality problems are very closely related to Stampacchia-type variational inequality problems. Particularly, Minty-type vector variational inequality problems are deeply connected with vector optimization problems. Liu et al. [10] considered vector variational inequalities for setvalued mappings by using scalarization approaches considered by Konnov [8]. Lee et al. [9] considered two kinds of Stampacchia-type vector variational inequalities by using four kinds of Stampacchia-type scalar variational inequalities and obtain the relations of the solution sets between the six variational inequalities, which are more generalized results than those considered in [10]. In this paper, the author considers the Minty-type case corresponding to the Stampacchia-type case considered in [9].

• Honam Mathematical Journal
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• v.32 no.2
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• pp.299-306
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• 2010

• Journal of the Korean Mathematical Society
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• v.37 no.5
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• pp.849-856
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• 2000

We give a new saddle point theorem for vector-valued functions on an admissible compact convex set in a topological vector space under weak condition that is the semicontinuity of two function scalarization and acyclicty of the involved sets. As application, we obtain the minimax theorem.

• Bulletin of the Korean Mathematical Society
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• v.52 no.6
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• pp.1777-1795
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• 2015

In this paper, we establish sufficient conditions for the solution set of parametric generalized vector mixed quasivariational inequality problem to have the semicontinuities such as the inner-openness, lower semicontinuity and Hausdorff lower semicontinuity. Moreover, a key assumption is introduced by virtue of a parametric gap function by using a nonlinear scalarization function. Then, by using the key assumption, we establish condition ($H_h$(${\gamma}_0$, ${\lambda}_0$, ${\mu}_0$)) is a sufficient and necessary condition for the Hausdorff lower semicontinuity, continuity and Hausdorff continuity of the solution set for this problem in Hausdorff topological vector spaces with the objective space being infinite dimensional. The results presented in this paper are different and extend from some main results in the literature.

• Journal of KIISE:Software and Applications
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• v.26 no.4
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• pp.557-567
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• 1999

본 논문은 데이터 캐시를 효과적으로 사용하기 위하여 개발된 원시 프로그램의 루프 변환체제에 대하여 논하고 있다. DIUS로 명명된 이 체계는 외부 루프 펼침을 중심으로 루프 분산, 교환이 선행되고 , 마직막에 스칼라화가 적용되는 변환체계이다. 루프 교환은 회전 공간이 루프 단위로 변형되어 전반적으로 캐시 재사용 기회를 높이지만 일부 배열 참조에 대해서는 오히려 재사용 기회를 감소시킨다. 본 연구에서는 이 문제를 외부 루프 펼침으로 해결하였다. 외부 루프 펼침과 루프 교환을 루프 몸체의 문장들에 선별적으로 적용하기 위하여 루프 분산을 도입하였다. 외부 루프 펼침을 적용하면 배열 참조를 스칼라 참조로 변환하는 스칼라화의 효과가 증대되어 레지스터 사용의 효율성이 높아진다. SPEC CFP95 벤치마크에 대하여 DIUS를 적용한 결과 기하학적 평균으로 속도 향상 1.10을 얻었으며, 특정 프로그램들은 모두 캐시 미스수가 줄어들었음을 확인하였다. 이와 같은 성능향상은사용된 루프 변환기법들이 갖는 캐시와 레지스터의 효율적인 사용에 기인한다.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.26 no.6
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• pp.987-992
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• 2002

In an attempt to solve multiobjective optimization problems, many traditional methods scalarize the objective vector into a single objective. In those cases, the obtained solution is highly sensitive to the weight vector used in the scalarization process and demands the user to have knowledge about the underlying problem. Moreover, in solving multiobjective problems, designers may be interested in a set of Pareto-optimal points, instead of a single point. In this paper, pareto-based Continuous Evolutionary Algorithms for Multiobjective Optimization problems having continuous search space are introduced. This algorithm is based on Continuous Evolutionary Algorithms to solve single objective optimization problems with a continuous function and continuous search space efficiently. For multiobjective optimization, a progressive reproduction operator and a niche-formation method fur fitness sharing and a storing process for elitism are implemented in the algorithm. The operator and the niche formulation allow the solution set to be distributed widely over the Pareto-optimal tradeoff surface. Finally, the validity of this method has been demonstrated through a numerical example.