• Environmental and Resource Economics Review
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• v.15 no.4
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• pp.673-692
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• 2006

In order to test for the dynamic optimality condition for the use of nonrenewable resource, it is necessary to estimate the shadow value of the resource in situ. In the previous literatures, a time series for in situ price has been derived either as the difference between marginal revenue and marginal cost or by differentiating with respect to the quantity of ore extracted the restricted cost function in which the quantity of ore is quasi-fixed. However, not only inconsistent estimates are likely to be generated due to the nonmalleability of capital, but the estimate of marginal revenue will be affected by market power. Since firms will likely fail to minimize the cost of the reproducible inputs subject to market prices under realistic circumstances where imperfect factor markets, strikes, or government regulations are present, the shadow in situ values obtained by estimating the restricted cost function can be biased. This paper provides a valid methodology for checking the dynamic optimality condition for a nonrenewable resource by using the input distance function. Our methodology has some advantages over previous ones: only data on quantities of inputs and outputs are required; nor is the maintained hypothesis of cost minimization required; adoption of linear programming enables us to circumvent autocorrelated errors problem caused by use of time series or panel data. The dynamic optimality condition for domestic coal mining does not hold for constant discount rates ranging from 2 to 20 percent over the period 1970~1993. The dynamic optimality condition also does not hold for variable rates ranging from fourth to four times the real interest rate.

• Journal of applied mathematics & informatics
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• v.27 no.1_2
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• pp.149-159
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• 2009

In this paper, we introduce some approximate optimal solutions and an augmented Lagrangian function in nonlinear programming, establish dual function and dual problem based on the augmented Lagrangian function, discuss the relationship between the approximate optimal solutions of augmented Lagrangian problem and that of primal problem, obtain approximate KKT necessary optimality condition of the augmented Lagrangian problem, prove that the approximate stationary points of augmented Lagrangian problem converge to that of the original problem. Our results improve and generalize some known results.

• Communications for Statistical Applications and Methods
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• v.15 no.2
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• pp.213-228
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• 2008

Using a linear loss function, this paper considers the one-sided testing problem for the exponential distribution via the empirical Bayes(EB) approach. Based on right censored data, we propose an EB test for the exponential parameter and obtain its convergence rate and asymptotic optimality, firstly, under the condition that the censoring distribution is known and secondly, that it is unknown.

• Bulletin of the Korean Mathematical Society
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• v.23 no.2
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• pp.141-148
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• 1986

In [1], M. Guignard considered a constraint set in a Banach space, which is similar to that in [2] and gave a first order necessary optimality condition which generalized the Kuhn-Tucker conditions [3]. Sufficiency is proved for objective functions which is either pseudoconcave [5] or quasi-concave [6] where the constraint sets are taken pseudoconvex. In this note, we consider a psedoconvex programming problem in a Hilbert space. Constraint set in a Hillbert space being pseudoconvex and the objective function is restrained by an operator equation. Then we use the methods similar to that in [1] and [6] to obtain a necessary and sufficient optimality condition.

• Nonlinear Functional Analysis and Applications
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• v.27 no.4
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• pp.813-837
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• 2022

In this paper we consider inverse problem for a general class of nonlinear stochastic differential equations on Hilbert spaces whose generating operators (drift, diffusion and jump kernels) are unknown. We introduce a class of function spaces and put a suitable topology on such spaces and prove existence of optimal generating operators from these spaces. We present also necessary conditions of optimality including an algorithm and its convergence whereby one can construct the optimal generators (drift, diffusion and jump kernel).

• International Journal of Control, Automation, and Systems
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• v.2 no.1
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• pp.15-22
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• 2004

Some recent advances in stability and optimality for the nonlinear receding horizon control (NRHC) or the nonlinear model predictive control (NMPC) are assessed. The NRHCs with terminal conditions are surveyed in terms of a terminal state equality constraint, a terminal cost, and a terminal constraint set. Other NRHCs without terminal conditions are surveyed in terms of a control Lyapunov function (CLF) and cost monotonicity. Additional approaches such as output feedback, fuzzy, and neural network are introduced. This paper excludes the results for linear receding horizon controls and concentrates only on the analytical results of NRHCs, not including applications of NRHCs. Stability and optimality are focused on rather than robustness.

• Journal of applied mathematics & informatics
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• v.26 no.1_2
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• pp.75-106
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• 2008

In this paper, we derive necessary optimality conditions for a continuous programming problem in which both objective and constraint functions contain support functions and is, therefore, nondifferentiable. It is shown that under generalized invexity of functionals, Karush-Kuhn-Tucker type optimality conditions for the continuous programming problem are also sufficient. Using these optimality conditions, we construct dual problems of both Wolfe and Mond-Weir types and validate appropriate duality theorems under invexity and generalized invexity. A mixed type dual is also proposed and duality results are validated under generalized invexity. A special case which often occurs in mathematical programming is that in which the support function is the square root of a positive semidefinite quadratic form. Further, it is also pointed out that our results can be considered as dynamic generalizations of those of (static) nonlinear programming with support functions recently incorporated in the literature.

• Journal of the military operations research society of Korea
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• v.25 no.2
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• pp.1-14
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• 1999

Metamodels using response surface methodology (RSM) are used for the optimality analysis of linear programming (LP). They have the form of a simple polynomial, and predict the optimal objective function value of an LP for various levels of the constraints. The metamodelling techniques for optimality analysis of LP can be applied to large-scale LP models. What is needed is some large-scale application of the techniques to verify how accurate they are. In this paper, we plan to use the large scale LP model, strategic transport optimal routing model (STORM). The developed metamodels of the large scale LP can provide some useful information.

• Journal of the Korean Institute of Intelligent Systems
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• v.12 no.1
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• pp.44-51
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• 2002

In order to generate hull form, fairness criteria applies to object function, B-spline curve vertices are considered as design variables, optimization is proceeded with satisfying geometric constraint conditions. GA(Genetic Algorithm) and optimality criteria apply to optimization process in this study.

• Journal of the Society of Naval Architects of Korea
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• v.39 no.4
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• pp.60-65
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• 2002

In order to generate hull form, we introduced optimization process. Fairness criteria is applied to object function, B-Spline control vertices are considered as design variables, optimization is proceeded with satisfying geometric constraint conditions. GA(Genetic Algorithm) and optimality criteria are applied to optimization process in this study.