• East Asian mathematical journal
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• v.36 no.1
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• pp.91-99
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• 2020

This paper obtains an explicit expression for a debtor's consumption, porfolio and time for filing for bankruptcy when the debtor is subject to upper bound on consumption rate. The utility of consumption is CRRA type and the dynamic programming principle is applied.

• Journal of the Chungcheong Mathematical Society
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• v.26 no.1
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• pp.85-90
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• 2013

We use the dynamic programming method to investigate the optimal consumption and investment problem with regime-switching. We derive the optimal solutions in closed-form with constant absolute risk aversion (CARA) utility.

• East Asian mathematical journal
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• v.35 no.3
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• pp.289-296
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• 2019

We establish necessary and sufficient optimality conditions for a nonsmooth fractional robust optimization programming problems. Moreover, we prove the weak and strong duality theorems under (V, ${\rho}$)-invexity assumption.

• Proceedings of the Korean Operations and Management Science Society Conference
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• 1994.04a
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• pp.504-504
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• 1994

• The Korean Journal of Applied Statistics
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• v.18 no.2
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• pp.421-434
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• 2005

Machine learning has been extensively studied in recent years as effective tools in pattern classification problem. Although there have been several approaches to machine learning, we focus on the mathematical programming (in particular, multi-objective and goal programming; MOP/GP) approaches in this paper. Among them, Support Vector Machine (SVM) is gaining much popularity recently. In pattern classification problem with two class sets, the idea is to find a maximal margin separating hyperplane which gives the greatest separation between the classes in a high dimensional feature space. However, the idea of maximal margin separation is not quite new: in 1960's the multi-surface method (MSM) was suggested by Mangasarian. In 1980's, linear classifiers using goal programming were developed extensively. This paper proposes a new family of SVM using MOP/GP techniques, and discusses its effectiveness throughout several numerical experiments.

• Journal of Electrical Engineering and Technology
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• v.3 no.3
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• pp.320-330
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• 2008

This paper presents an improved dynamic programming (IDP) approach to solve the economic power dispatch problem including transmission losses in power systems. A detailed mathematical derivation of recursive dynamic programming approach for the economic power dispatch problem with transmission losses is presented. The transmission losses are augmented with the objective function using price factor. The generalized expression for optimal scheduling of thermal generating units derived in this article can be implemented for the solution of the economic power dispatch problem of a large-scale system. Six-unit, fifteen-unit, and forty-unit sample systems with non-linear characteristics of the generator, such as ramp-rate limits and prohibited operating zones are considered to illustrate the effectiveness of the proposed method. The proposed method results have been compared with the results of genetic algorithm and particle swarm optimization methods reported in the literature. Test results show that the proposed IDP approach can obtain a higher quality solution with better performance.

• Journal of the Korean Operations Research and Management Science Society
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• v.6 no.1
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• pp.57-64
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• 1981

The continuous increase of crude oil consumption has struck great impact into the world economy, When we consider disadvantageous articles in contract for oil import, it would be desirable to import in batch the total quantity of crude oil contracted, but which is not available under the present situation which has many constraints This paper treats of the ways to deliver the crude oil in a given period so as to maximize the profit derived from the sales of oil products, To do this we should consider the prices of crude oil and oil products, inventory cost, transportation cost, oil refinement cost, and fluctuations of these parameters in a given period. The case of Korea Oil Corporation is treated in this paper to generalize the problem of crude oil transportation from Middle East and formulated in a mathematical programming. This programming is transformed into Dynamic Programming through specifing states, stages, payoffs, and recursive function. To clarify these procedure and methods, the case of Korea Oil Corporation is dealt with again and demonstrated in detail.

• Journal of Korean Institute of Industrial Engineers
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• v.23 no.1
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• pp.39-54
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• 1997

This paper presents four process models for machining processes : 1) an economical mathematical model of machining process, 2) a prediction model for surface roughness, 3) a decision model for fuzzy cutting conditions, and 4) a judgment model of machinability with automatic selection of cutting conditions. Each model was developed the economic machining, and these models were applied to theories widely studied in industrial engineering which are nonlinear programming, computer simulation, fuzzy theory, and neural networks. The results of this paper emphasize the human oriented domain of a nonlinear programming problem. From a viewpoint of the decision maker, fuzzy nonlinear programming modeling seems to be apparently more flexible, more acceptable, and more reliable for uncertain, ill-defined, and vague problem situations.

• 전기의세계
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• v.30 no.6
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• pp.375-385
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• 1981

New algorithms are derived for nonlinear programming problems which are characterized by their large variables and equality and inequality constraints. The algorithms are based upon the introduction of the Dependent-Variable-Elimination method, Independent-Variable-Reduction method, Optimally-Ordered-Triangular-Factorization method, Equality-Inequality-Sequential-Satisfaction method, etc. For a case study problem relating to the optimal determination of load flow in a 10-bus, 13-line sample power system, several approaches are undertaken, such as SUMT, Lagrange's Multiplier method, sequential applications of linear and quadratic programming method. For applying the linear programming method, the conventional simplex algorithm is modified to the large-system-oriented one by the introduction of the Two-Phase method and Variable-Upper-Bounding method, thus resulting in remarkable savings in memory requirements and computing time. The case study shows the validity and effectivity of the algorithms presented herein.

• Communications of Mathematical Education
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• v.19 no.4 s.24
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• pp.823-837
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• 2005

[ $T_EX$ ] is a typesetting system created by Donald E. Knuth for producing publication-quality scientific books and journals. It is famous for the line breaking algorithm, the formatting of complex mathematical formula, and the powerful macro programming capability. Recently $T_EX$ plays a new role of an automatic typesetting engine. The paper describes $T_EX$ in the framework of typography by comparing with DTP softwares and word processors.