• Bulletin of the Korean Mathematical Society
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• v.26 no.2
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• pp.127-134
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• 1989

This paper proposes a deformation method for solving practical nonlinear programming problems. Utilizing the nonlinear parametric programming technique with Quasi-Newton method [6,7], the method solves the problem by imbedding it into a suitable one-parameter family of problems. The approach discussed in this paper was originally developed with the aim of solving a system of structural optimization problems with frequently appears in various kind of engineering design. It is assumed that we have to solve more than one structural problem of the same type. It an optimal solution of one of these problems is available, then the optimal solutions of thel other problems can be easily obtained by using this known problem and its optimal solution as the initial problem of our parametric method. The method of nonlinear programming does not generally converge to the optimal solution from an arbitrary starting point if the initial estimate is not sufficiently close to the solution. On the other hand, the deformation method described in this paper is advantageous in that it is likely to obtain the optimal solution every if the initial point is not necessarily in a small neighborhood of the solution. the Jacobian matrix of the iteration formula has the special structural features [2, 3]. Sectioon 2 describes nonlinear parametric programming problem imbeded into a one-parameter family of problems. In Section 3 the iteration formulas for one-parameter are developed. Section 4 discusses parametric approach for Quasi-Newton method and gives algorithm for finding the optimal solution.

• The KIPS Transactions:PartD
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• v.8D no.4
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• pp.421-426
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• 2001

A formal development method is used to develop software rigorously and systematically. In a formal development method, we specify system by a formal specification language and gradually develop the system more concretely until we can implement the system. VDM is one of formal specification languages. VDM uses mathematical data structures such as sets, sequences, and maps to specify the system, but most programming languages do not have such data structures. Therefore, these data structures should be converted. We can convert mathematical data structures in VDM to a linked list, a data structure in a programming language. In this article, we propose a method to convert a set, a sequence, and a map in VDM to a linked list in a programming language and prove the correctness of this conversion mathematically.

• Industrial Engineering and Management Systems
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• v.11 no.2
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• pp.183-187
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• 2012

In this paper, we study the fixed charge transportation problem with uncertain variables. The fixed charge transportation problem has two kinds of costs: direct cost and fixed charge. The direct cost is the cost associated with each source-destination pair, and the fixed charge occurs when the transportation activity takes place in the corresponding source-destination pair. The uncertain fixed charge transportation problem is modeled on the basis of uncertainty theory. According to inverse uncertainty distribution, the model can be transformed into a deterministic form. Finally, in order to solve the uncertain fixed charge transportation problem, a numerical example is given to show the application of the model and algorithm.

• IE interfaces
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• v.21 no.1
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• pp.1-7
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• 2008

In this paper we study the Minimum Edge Addition Problem(MEAP) to decrease the diameter of a graph. MEAP can be used for improving the serviceability of telecommunication networks with a minimum investment. MEAP is an NP-hard optimization problem. We present two mathematical programming models : One is a multi-commodity flow formulation and the other is a path partition formulation. We propose a branch-and-price algorithm to solve the path partition formulation to the optimality. We develop a polynomial time column generation sub-routine conserving the mathematical structure of a sub problem for the path partition formulation. Computational experiments show that the path partition formulation is better than the multi-commodity flow formulation. The branch-and-price algorithm can find the optimal solutions for the immediate size graphs within reasonable time.

• Structural Engineering and Mechanics
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• v.62 no.3
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• pp.303-310
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• 2017

The model updating problems, which are to find the optimal approximation to the discrete quadratic model obtained by the finite element method, are critically important to the vibration analysis. In this paper, the structured model updating problem is considered, where the coefficient matrices are required to be symmetric and positive semidefinite, represent the interconnectivity of elements in the physical configuration and minimize the dynamics equations, and furthermore, due to the physical feasibility, the physical parameters should be positive. To the best of our knowledge, the model updating problem involving all these constraints has not been proposed in the existed literature. In this paper, based on the semidefinite programming technique, we design a general-purpose numerical algorithm for solving the structured model updating problems with incomplete measured data and present some numerical results to demonstrate the effectiveness of our method.

• Journal of the Korean Operations Research and Management Science Society
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• v.6 no.1
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• pp.15-23
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• 1981

This paper deals with cross impact analysis for technology assessment. The focus of the paper is to develop new technique of cross impact matrix using goal programming method. In this study, the idea of cross impact analysis based on scenario generation method especially SMIC-74 (2) is expanded. Critical literature review on SMIC-74 is presented to discuss the mathematical rationale of consistent probability in cross impact analysis. A new model of cross impact analysis using goal programming to overcome the shortcomings of the scenario generation technique especially SMIC-74 is developed. This new technique is also applied to the assessment of the air pollution problems in Seoul Metropolitan area in Korea. The results of analysis give us following findings 1) Cross impact analysis using goal programming produce more meaningful solutions comparing to those of SMIC-74 2) Theoretical rationale of the objective function in the newly developed technique is more appropriate than that of SMIC-74.

• Journal of Fisheries and Marine Sciences Education
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• v.25 no.5
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• pp.1020-1030
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• 2013

The purpose of this study was to develop the STEAM educational program based on the computer programming. STEAM education has been recently attracted to a lot of people. We had a focus of computer science in STEM fields. We used the programming language f or learning KODU. We selected appropriate topics for STEAM education and learning programming. We developed the educational program of 30 hours about selected topics and had classes for 4th and 5th grade elementary students. In order to verify the effectiveness of the educational program, we analyzed the results of pre- and posttest about GALT(Group Assessment of Logical Thinking), TTCT(Torrance Tests of Creative Thinking), science-related affective domain, and mathematical interests and attitudes tests. In the analysis results, the education program we developed had positive impacts on creativity, logical thinking, and science-related affective domain of elementary school students.

• Honam Mathematical Journal
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• v.28 no.4
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• pp.521-531
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• 2006

In this paper, we construct a procedure of Maple programming for (0, 1)-matrix with a prescribed permanent, $1,2,...,2^{n-1}$. An application of such construction is given, and we obtain the some results of (0, 1)-matrices with the permanent less than or equal to n! by replacing elements 0's by 1's.

• Journal of the Chungcheong Mathematical Society
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• v.27 no.2
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• pp.219-225
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• 2014

I use the dynamic programming approach to study the optimal consumption and investment problem with regime-switching and constant labor income. I derive the optimal solutions in closed-form with constant absolute risk aversion (CARA) utility and constant disutility.

• Communications of the Korean Mathematical Society
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• v.19 no.1
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• pp.179-196
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• 2004

Mond-Weir type duals for multiobjective variational problems are formulated. Under generalized vector variational type I invexity assumptions on the functions involved, sufficient optimality conditions, weak and strong duality theorems are proved efficient and properly efficient solutions of the primal and dual problems.