• 대한수학회지
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• 제44권4호
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• pp.971-985
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• 2007

A sequential optimality condition characterizing the efficient solution without any constraint qualification for an abstract convex vector optimization problem is given in sequential forms using subdifferentials and ${\epsilon}$-subdifferentials. Another sequential condition involving only the subdifferentials, but at nearby points to the efficient solution for constraints, is also derived. Moreover, we present a proposition with a sufficient condition for an efficient solution to be properly efficient, which are a generalization of the well-known Isermann result for a linear vector optimization problem. An example is given to illustrate the significance of our main results. Also, we give an example showing that the proper efficiency may not imply certain closeness assumption.

• International Journal of Reliability and Applications
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• 제17권1호
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• pp.21-49
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• 2016

Many mechanical, electrical and electronic products have more than one performance characteristics (PCs). For example the performance degradation of rubidium discharge lamps can be characterized by the rubidium consumption or the decreasing intensity the lamp. The product may degrade due to all the PCs which may be independent or dependent. This paper deals with the design of optimal bivariate step-stress partially accelerated degradation test (PADT) with degradation paths modelled by gamma process. The dependency between PCs has been modelled through Frank copula function. In partial step-stress loading, the unit is tested at usual stress for some time, and then the stress is accelerated. This helps in preventing over-stressing of the test specimens. Failure occurs when the performance characteristic crosses the critical value the first time. Under the constraint of total experimental cost, the optimal test duration and the optimal number of inspections at each intermediate stress level are obtained using variance optimality criterion.

• Journal of applied mathematics & informatics
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• 제17권1_2_3호
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• pp.379-390
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• 2005

In this paper, optimality conditions for multiobjective programming problems having F-convex objective and constraint functions are considered. An equivalent multiobjective programming problem is constructed by a modification of the objective function. Furthermore, an F-Lagrange function is introduced for a constructed multiobjective programming problem, and a new type of saddle point is introduced. Some results for the new type of a saddle point are given.

• 대한수학회논문집
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• 제20권4호
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• pp.837-847
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• 2005

We consider multiobjective fractional programming problems with generalized invexity. An equivalent multiobjective programming problem is formulated by using a modification of the objective function due to Antczak. We give relations between a multiobjective fractional programming problem and an equivalent multiobjective fractional problem which has a modified objective function. And we present modified vector saddle point theorems.

• 대한수학회보
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• 제45권3호
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• pp.563-571
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• 2008

We deduce the necessary conditions for the optimality of endpoint constrained optimal control problem. These conditions comprise the adjoint equation, the maximum principle and the transversality condition. We assume that the cost function is merely differentiable. Therefore the technique under Lipschitz continuity hypothesis is not directly applicable. We introduce Fermat's rule and value function technique to obtain the results.

• Korean Journal of Mathematics
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• 제23권2호
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• pp.283-291
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• 2015

In the optimal control problem, at first we search the expected optimal solution by using Pontryagin type's necessary conditions called the maximum principle. Next we use the sufficient conditions to conclude that the searched solution is optimal. In this article the sufficient conditions are studied. The value function is used for sufficient conditions.

• 한국항공우주학회지
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• 제37권4호
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• pp.367-371
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• 2009

본 논문에서는 기존 연구결과들과 달리 비행체의 운동을 선형방정식으로 표현할 수 있다는 가정을 도입하지 않고 비례항법유도법칙의 최적성에 관한 해석 결과를 제시한다. 비례항법유도법칙은 비행체-표적 거리의 지수함수를 가중치로 갖는 제어 에너지를 최소화하는 최적의 유도법칙임을 비선형 방정식 기반으로 유도한다. 이때 가중함수의 지수와 비례항법상수와의 관계에 대해 설명한다. 또한 이러한 해석의 유효한 조건을 도출한다.

• Interaction and multiscale mechanics
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• 제5권3호
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• pp.211-228
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• 2012

This paper reports the development of a generalized inverse analysis formulation for the parameter estimation of four-parameter Burger model. The analysis is carried out by formulating the problem as a mathematical programming formulation in terms of identification of the design vector, the objective function and the design constraints. Thereafter, the formulated constrained nonlinear multivariable problem is solved with the aid of fmincon: an in-built constrained optimization solver module available in MatLab. In order to gain experience, a synthetic case-study is considered wherein key issues such as the determination and setting up of variable bounds, global optimality of the solution and minimum number of data-points required for prediction of parameters is addressed. The results reveal that the developed technique is quite efficient in predicting the model parameters. The best result is obtained when the design variables are subjected to a lower bound without any upper bound. Global optimality of the solution is achieved using the developed technique. A minimum of 4-5 randomly selected data-points are required to achieve the optimal solution. The above technique has also been adopted for real-time settlement of four oil refineries with encouraging results.

• 한국경영과학회지
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• 제13권2호
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• pp.66-71
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• 1988

Let B be present value of some sequence. This paper concerns the maximization of the expected utility of the present value B when the utility function is exponential.

• Communications for Statistical Applications and Methods
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• 제2권2호
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• pp.376-386
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• 1995

Designs for polynomial approximation to the unknown response function are considered. Optimality criteria are monotone functions of the mean squared error matrix of the least squares estimator. They correspond to the classical A-, D-, G- and Q-optimalities. Optimal first order designs are chosen from the invariant designs and then compared with optimal second order designs.