• 대한수학회논문집
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• 제25권1호
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• pp.139-147
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• 2010

A generalized nondifferentiable fractional optimization problem (GFP), which consists of a maximum objective function defined by finite fractional functions with differentiable functions and support functions, and a constraint set defined by differentiable functions, is considered. Recently, Kim et al. [Journal of Optimization Theory and Applications 129 (2006), no. 1, 131-146] proved optimality theorems and duality theorems for a nondifferentiable multiobjective fractional programming problem (MFP), which consists of a vector-valued function whose components are fractional functions with differentiable functions and support functions, and a constraint set defined by differentiable functions. In fact if $\overline{x}$ is a solution of (GFP), then $\overline{x}$ is a weakly efficient solution of (MFP), but the converse may not be true. So, it seems to be not trivial that we apply the approach of Kim et al. to (GFP). However, modifying their approach, we obtain optimality conditions and duality results for (GFP).

• 한국전산구조공학회:학술대회논문집
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• 한국전산구조공학회 2005년도 춘계 학술발표회 논문집
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• pp.89-96
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• 2005

Numerical procedure of design optimality evaluation is studied for caisson structural systems. Two kinds of evaluation methods can be considered; mathematical optimality criteria method (MOCM) and numerical optimization method (NOM). The choice of the method depends on the available information of the system MOCM can be used only when the information of all function values, gradients and Lagrange multipliers is available, which may not be realistic in practice. Therefore, in this study, NOMs are applied for the structural optimality evaluation, where only design variables are necessary. To this end, Metropolis genetic algorithm (MGA) is advantageously used and applied for a standard optimization model of caisson composite breakwater. In the numerical example, cost and constraint functions are assumed to be changed from the orignal design situation and their effects are evaluated for optimality. From the theoretical consideration and numerical experience, it is found that the proposed optimality evaluation procedure with MGA-based NOM is efficient and practically applicable.

• 충청수학회지
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• 제26권4호
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• pp.723-734
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• 2013

A robust optimization problem, which has a maximum function of continuously differentiable functions as its objective function, continuously differentiable functions as its constraint functions and a geometric constraint, is considered. We prove a necessary optimality theorem and a sufficient optimality theorem for the robust optimization problem. We formulate a Wolfe type dual problem for the robust optimization problem, which has a differentiable Lagrangean function, and establish the weak duality theorem and the strong duality theorem which hold between the robust optimization problem and its Wolfe type dual problem. Moreover, saddle point theorems for the robust optimization problem are given under convexity assumptions.

• 한국통신학회논문지
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• 제30권2B호
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• pp.21-26
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• 2005

효율적인 통신망에서의 라우팅을 위해, 개선된 에너지 함수를 가지는 Hopfield 신경망에 의한 알고리즘이 본 논문에서 제안되었는데, 보다 높은 최적경로 형성과 안정적 수렴의 결과를 목적으로 한다. 20-50 개의 노드를 가지며, 무작위 연결 비용이 인가되는 3,000 개의 통신망에 대한 실험의 결과에서 볼 때, 기존의 신경망을 이용한 알고리즘들이 노드 수가 많은 망 환경에서 수렴하지 않거나, 최적경로가 형성이 되지 않은 경우가 많았지만 제안된 알고리즘은 최적경로 형성에서 기존 알고리즘 보다 약 65%의 개선을 하였고 또한 기존 알고리즘 보다 약 50% 정도 수렴이 잘 되는 것이 확인되었다.

• 대한수학회지
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• 제43권2호
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• pp.241-258
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• 2006

This paper gives conditions under which necessary optimality conditions in a locally Lipschitz program can be expressed as the invexity of the active constraint functions or the type I invexity of the objective function and the constraint functions on the feasible set of the program. The results are nonsmooth extensions of those of Hanson and Mond obtained earlier in differentiable case.

• Management Science and Financial Engineering
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• 제18권1호
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• pp.21-26
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• 2012

Two previous studies that attempted to generalize the deterministic joint pricing-inventory decision model are reevaluated. We prove analytically that even in a single-product environment, the EOQ model with constant priceelastic demand cannot find optimal solutions unless two optimality conditions associated with price elasticity and demand magnitude are satisfied. Due to the inexistence of the general optimality for the problem, demand function and price elasticity must be evaluated and bounded properly to use the methods proposed in the previous studies.

• Journal of applied mathematics & informatics
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• 제18권1_2호
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• pp.539-551
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• 2005

In this paper, sufficient optimality conditions and duality results for nonsmooth vector optimization problems are given under near invexity and infineness assumptions. Also, weak vector saddle-point theorems are obtained under near invexity-infineness assumptions.

• Journal of applied mathematics & informatics
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• 제22권1_2호
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• pp.425-434
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• 2006

The process of producing 1,3-preprandiol by microorganism continuous cultivation would attain its equilibrium state. How to get the highest concentration of 1,3-propanediol at that time is the aim for producers. Based on this fact, an optimization model is introduced in this paper, existence of optimal solution is proved. By infinite-dimensional optimal theory, the optimal condition of model is given and the equivalence between optimal condition and the zero of optimality function is proved.

• Journal of applied mathematics & informatics
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• 제10권1_2호
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• pp.83-99
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• 2002

Optimality conditions are derived for a nonlinear program in which a support function appears in the objective as well as in each constraint function. Wolfe and Mond-Weir type duals to this program are presented and various duality results are established under suitable convexity and generalized convexity assumptions. Special cases that often occur in the literature are those in which a support function is the square root of a positive semi- definite quadratic form or an Lp norm. It is pointed out that these special cases can easily be generated from our results.

• Management Science and Financial Engineering
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• 제7권1호
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• pp.41-56
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• 2001

This linear fractional - quadratic bilevel programming problem, in which the leader's objective function is a linear fractional function and the follower's objective function is a quadratic function, is studied in this paper. The leader's and the follower's variables are related by linear constraints. The derivations of the optimality conditions are based on Kuhn-Tucker conditions and the duality theory. It is also shown that the original linear fractional - quadratic bilevel programming problem can be solved by solving a standard linear fractional program and the optimal solution of the original problem can be achieved at one of the extreme point of a convex polyhedral formed by the new feasible region. The algorithm is illustrated with the help of an example.