• 대한수학회지
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• 제48권5호
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• pp.985-999
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• 2011

A new filled function method is presented in this paper to solve box-constrained nonlinear integer programming problems. It is shown that for a given non-global local minimizer, a better local minimizer can be obtained by local search starting from an improved initial point which is obtained by locally solving a box-constrained integer programming problem. Several illustrative numerical examples are reported to show the efficiency of the present method.

• 대한수학회보
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• 제42권4호
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• pp.837-849
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• 2005

In this paper, we obtain a successive quadratic programming algorithm for solving the semidefinite programming (SDP) relaxation of the binary quadratic programming. Combining with a randomized method of Goemans and Williamson, it provides an efficient approximation for the binary quadratic programming. Furthermore, its convergence result is given. At last, We report some numerical examples to compare our method with the interior-point method on Maxcut problem.

• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 1996년도 Proceedings of the Korea Automatic Control Conference, 11th (KACC); Pohang, Korea; 24-26 Oct. 1996
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• pp.215-218
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• 1996

In work scheduling problems, scheduling constraints are not absolutely rigid; they may be changed depending on the scheduling aspect effected. In order to cope with changes in scheduling constraints and assignment strategies and to optimize scheduling results quickly, this paper will propose a new scheduling method which combines knowledge engineering and mathematical programming techniques.

• East Asian mathematical journal
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• 제35권5호
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• pp.597-612
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• 2019

In this study, we propose a new logarithmic barrier approach to solve linear programming problem using the projective method of Karmarkar. We are interested in computation of the direction by Newton's method and of the step-size using minorant functions instead of line search methods in order to reduce the computation cost. Our new approach is even more beneficial than classical line search methods. We reinforce our purpose by many interesting numerical simulations proved the effectiveness of the algorithm developed in this work.

• East Asian mathematical journal
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• 제28권3호
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• pp.293-303
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• 2012

Sequential quadratic programming (SQP) has been one of the most important methods for solving nonlinear constrained optimization problems. Recently, filter method, proposed by Fletcher and Leyffer, has been extensively applied for its promising numerical results. In this paper, we present and study an active set SQP-filter algorithm for inequality constrained optimization. The active set technique reduces the size of quadratic programming (QP) subproblem. While by the filter method, there is no penalty parameter estimate. Moreover, Maratos effect can be overcome by filter technique. Global convergence property of the proposed algorithm are established under suitable conditions. Some numerical results are reported in this paper.

• 한국공간구조학회:학술대회논문집
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• 한국공간구조학회 2008년도 춘계 학술발표회 논문집
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• pp.101-106
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• 2008

본 연구에서는 서로 상이한 최적화기법인 유전알고리듬과 수학적 프로그래밍기법을 이용하여 지오데식 돔 구조물을 최적화하고 그 결과를 분석하였다. 본 연구에서 도입한 유전알고리즘은 유전연산자인 선택, 교배, 돌연변이 이외에도 재생기법을 도입하여 최적해의 검색성능을 높였다. 그리고 수학적인 프로그래밍기법은 유한차분법을 이용하여 목적함수의 설계민감도를 계산하였으며 세 가지의 다른 검색기법을 이용하여 돔의 크기최적화를 수행하였다. 지오데식 돔의 중앙에 작용하는 집중하중에 저항하는 돔의 각 부재의 크기패턴을 자체 개발된 $ISADO-GA{\alpha}$와 ISADO-OPT를 이용하여 최적 설계하였다. 본 연구를 통하여 제시된 최적결과는 정해가 존재하지 않는 실제 구조물의 최적 값에 대한 유용한 정보를 제공할 뿐만이 아니라 향후 대공간구조의 새로운 구조시스템 개발의 밑거름이 될 것으로 판단된다.

• 한국산림과학회지
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• 제76권4호
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• pp.361-369
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• 1987

다목적(多目的) 산지이용(山地利用)은 산지이용(山地利用)의 효율성(效率性)을 제고(提高)하기 위한 경제학(經濟學)의 한 응용분야로서, 외국(外國)에서 임업경영(林業經營)에 널리 사용(使用)하는 기법(技法)이다. 본고(本稿)에서는 다목적(多目的) 경영(經營)을 위해 사용(使用)되는 수리계획법(數理計劃法)의 일종인 STEM과 제약조건법(制約條件法)을 임업분야(林業分野)에 도입 적용하여 가상자료에 의거 이들 방법간(方法間)의 장(長) 단점(短點)을 비교(比較) 검토(檢討)하였다.

• 충청수학회지
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• 제25권2호
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• pp.277-281
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• 2012

I study an optimal consumption and portfolio selection problem with regime-switching using a dynamic programming method. With constant relative risk aversion (CRRA) utility I obtain optimal solutions in closed-form.

• Communications for Statistical Applications and Methods
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• 제12권1호
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• pp.181-189
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• 2005

This paper suggest a method of inclusion probability proportional to size sampling that provides a non-negative and stable variance estimator. The sampling procedure is quite simple and flexible since a sampling design is easily obtained using mathematical programming. This scheme appears to be preferable to Nigam, Kumar and Gupta's (1984) method which uses a balanced incomplete block designs. A comparison is made with their method through an example in the literature.

• Journal of Mechanical Science and Technology
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• 제17권10호
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• pp.1496-1506
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• 2003

The SIMP (solid isotropic material with penalization) approach is perhaps the most popular density variable relaxation method in topology optimization. This method has been very successful in many applications, but the optimization solution convergence can be improved when new variables, not the direct density variables, are used as the design variables. In this work, we newly propose S-shape functions mapping the original density variables nonlinearly to new design variables. The main role of S-shape function is to push intermediate densities to either lower or upper bounds. In particular, this method works well with nonlinear mathematical programming methods. A method of feasible directions is chosen as a nonlinear mathematical programming method in order to show the effects of the S-shape scaling function on the solution convergence.