• Journal of applied mathematics & informatics
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• v.6 no.1
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• pp.111-126
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• 1999

The article is devoted to mathematical modeling of prob-lems of stochastic optimization of the plastic metal working. Classifi-cation and mathematical statements of such problems are proposed. Several calculation techniques of the single goal function are pre-sented. The probability theory and the Fuzzy numbers were applied for solution of the problems of stochastic optimization.

• East Asian mathematical journal
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• v.31 no.3
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• pp.371-377
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• 2015

We consider a nondifferentiable robust optimization problem, which has a maximum function of continuously differentiable functions and support functions as its objective function, continuously differentiable functions as its constraint functions. We prove optimality conditions for the nondifferentiable robust optimization problem. We formulate a Wolfe type dual problem for the nondifferentiable robust optimization problem and prove duality theorems.

• East Asian mathematical journal
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• v.37 no.5
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• pp.543-551
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• 2021

Recently, semidefinite optimization problems have been intensively studied since many optimization problem can be changed into the problems and the the problems are very computationable. In this paper, we consider a semidefinite linear vector optimization problem (VP) and we establish the optimality theorems for (VP), which holds without any constraint qualification.

• Journal of Korean Society of Transportation
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• v.12 no.3
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• pp.5-13
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• 1994

In the fields of rail and road design, most vertical alignment design have been thus far heavily dependent upon trial-and-errors of experienced engineers. However, it has long been inefficient in productivity of designing process. In order to overcome this inefficiency, this paper presents the optimal vertical alignment design method using mathematical optimization techniques. For optimization, mathematical model to minimize the construction cost is formulated and the separable programming technique and the Zoutendijk method are introduced to solve it. As result, it is shown that this optimization technique can give efficient solutions to all vertical alignment design fields with properly-estimated cost function.

• East Asian mathematical journal
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• v.31 no.5
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• pp.737-742
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• 2015

In this paper, we consider a generalized fractional robust optimization problem (FP). Establishing a nonfractional optimization problem (NFP) equivalent to (FP), we establish necessary optimality conditions and duality results.

• East Asian mathematical journal
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• v.31 no.3
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• pp.345-349
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• 2015

In this paper, we consider a fractional robust optimization problem (FP) and give necessary optimality theorems for (FP). Establishing a nonfractional optimization problem (NFP) equivalent to (FP), we formulate a Mond-Weir type dual problem for (FP) and prove duality theorems for (FP).

• Journal of applied mathematics & informatics
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• v.7 no.2
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• pp.507-516
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• 2000

In the present paper we consider a problem of choosing the rational way to carry on the metal processing (the problem of stochastic optimization) and the problem of determing the unknown characteristics of parameters described with random variables.

• Journal of the Korean Society of Marine Environment & Safety
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• v.23 no.3
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• pp.258-265
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• 2017

This paper validates a system identification method using mathematical optimization using sea trial measurement data as a benchmark. A fast time simulation tool, SIMOPT, and a Rheinmetall Defence mathematical model have been adopted to conduct initial hydrodynamic coefficient estimation and simulate ship modelling. Calibration for the environmental effect of sea trial measurement and sensitivity analysis have been carried out to enable a simple and efficient optimization process. The optimization process consists of three steps, and each step controls different coefficients according to the corresponding manoeuvre. Optimization result of Step 1, an optimization for coefficient on x-axis, was similar compared to values applying an empirical regression formulae by Clarke and Norrbin, which is used for SIMOPT. Results of Steps 2 and 3, which are for linear coefficients and nonlinear coefficients, respectively, was differ from the calculation results of the method by Clarke and Norrbin. A comparison for ship trajectory of simulation results from the benchmark and optimization results indicated that the suggested stepwise optimization method enables a coefficient tuning in a mathematical way.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 2005.06a
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• pp.822-827
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• 2005

Recently engineering systems problems become quite large and complicated. For those problems, design requirements are fairly complex. It is not easy to design such systems by considering only one discipline. Therefore, we need a design methodology that can consider various disciplines. Multidisciplinary Design Optimization (MDO) is an emerging optimization method to include multiple disciplines. So far, about seven MDO methodologies have been proposed for MDO. They are Multidisciplinary Feasible (MDF), Individual Feasible (IDF), All-at-Once (AAO), Concurrent Subspace Optimization (CSSO), Collaborative Optimization (CO), Bi-Level Integrated System Synthesis (BLISS) and Multidisciplinary Optimization Based on Independent Subspaces (MDOIS). In this research, the performances of the methods are evaluated and compared. Practical engineering problems may not be appropriate for fairness. Therefore, mathematical problems are developed for the comparison. Conditions for fair comparison are defined and the mathematical problems are defined based on the conditions. All the methods are coded and the performances of the methods are compared qualitatively as well as quantitatively.

• Journal of the Korean Mathematical Society
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• v.40 no.2
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• pp.287-305
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• 2003

Second order necessary optimality condition for properly efficient solutions of a twice differentiable vector optimization problem is given. We obtain a nonsmooth version of the second order necessary optimality condition for properly efficient solutions of a nondifferentiable vector optimization problem. Furthermore, we prove a second order necessary optimality condition for weakly efficient solutions of a nondifferentiable vector optimization problem.