• 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.

• Journal of the Korean Mathematical Society
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• v.43 no.2
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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.

• Journal of the Korean Mathematical Society
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• v.37 no.4
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• pp.625-643
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• 2000

In this paper we formulate an optimal control problem governed by time-delay Volterra integral equations; the problem includes control constraints as well as terminal equality and inequality constraints on the terminal state variables. First, using a special type of state and control variations, we represent a relatively simple and self-contained method for deriving new necessary conditions in the form of Pontryagin minimum principle. We show that these results immediately yield classical Pontryagin necessary conditions for control processes governed by ordinary differential equations (with or without delay). Next, imposing suitable convexity conditions on the functions involved, we derive Mangasarian-type and Arrow-type sufficient optimality conditions.

• 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.

• Journal of applied mathematics & informatics
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• v.29 no.5_6
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• pp.1157-1165
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• 2011

The Karush-Kuhn-Tucker (KKT) necessary optimality conditions for nonlinear differentiable programming problems are also sufficient under suitable convexity assumptions. The KKT conditions in multiobjective programming problems with interval-valued objective and constraint functions are derived in this paper. The main contribution of this paper is to obtain the Pareto optimal solutions by resorting to the sufficient optimality condition.

• Journal of applied mathematics & informatics
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• v.18 no.1_2
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• pp.273-286
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• 2005

Parameter identification problem of a three species (predator, mutualist-prey, and mutualist) ecological system with reaction-diffusion phenomenon is investigated in this paper. The mathematical model of the parameter identification problem is constructed and continuous dependence of the solution for the direct problem on the parameters identified is obtained. Finally, the existence of optimal solution and an optimality necessary condition for the parameter identification problem are given.

• Journal of applied mathematics & informatics
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• v.27 no.1_2
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• pp.365-374
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• 2009

Under certain conditions, we use augmented Lagrangians to transform a class of generalized semi-infinite min-max problems into common semi-infinite min-max problems, with the same set of local and global solutions. We give two conditions for the transformation. One is a necessary and sufficient condition, the other is a sufficient condition which can be verified easily in practice. From the transformation, we obtain a new first-order optimality condition for this class of generalized semi-infinite min-max problems.

• 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.

• 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 the Korean Mathematical Society
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• v.43 no.5
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• pp.931-950
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• 2006

We study the identification problems of constant parameters appearing in the perturbed sine-Gordon equation with the Neumann boundary condition. The existence of optimal parameters is proved, and necessary conditions are established for several types of observations by utilizing quadratic optimal control theory due to Lions [13].