• 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 the Chungcheong Mathematical Society
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• v.30 no.1
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• pp.31-40
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• 2017

In this paper, we consider a nonsmooth multiobjective robust optimization problem with more than two locally Lipschitz objective functions and locally Lipschitz constraint functions in the face of data uncertainty. We prove a nonsmooth sufficient optimality theorem for a weakly robust efficient solution of the problem. We formulate a Wolfe type dual problem for the problem, and establish duality theorems which hold between the problem and its Wolfe type dual problem.

• Journal of the Korean Mathematical Society
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• v.36 no.1
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• pp.173-192
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• 1999

We study a boundary optimal control problem of the fluid flow governed by the Navier-Stokes equations. the control problem is formulated with the flow through a channel with steps. The first-order optimality condition of the optimal control is derived. Finite element approximations of the solutions of the optimality system are defined and optimal error estimates are derived. finally, we present some numerical results.

• 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).

• Journal of applied mathematics & informatics
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• v.20 no.1_2
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• pp.209-224
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• 2006

This paper presents an optimization model with performance constraints for two kinds of graph elements layout problem. The layout problem is partitioned into finite subproblems by using graph theory and group theory, such that each subproblem overcomes its on-off nature about optimal variable. Furthermore each subproblem is relaxed and the continuity about optimal variable doesn't change. We construct a min-max problem which is locally equivalent to the relaxed subproblem and develop the first order necessary and sufficient conditions for the relaxed subproblem by virtue of the min-max problem and the theories of convex analysis and nonsmooth optimization. The global optimal solution can be obtained through the first order optimality conditions.

• 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 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.

• Communications of the Korean Mathematical Society
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• v.35 no.4
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• pp.1329-1352
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• 2020

In this paper we consider a class of nonlinear evolution equations on infinite dimensional Banach spaces driven by vector measures. We prove existence and uniqueness of solutions and continuous dependence of solutions on the control measures. Using these results we prove existence of optimal controls for Bolza problems. Based on this result we present necessary conditions of optimality.

• International Journal of Advanced Culture Technology
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• v.10 no.4
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• pp.576-582
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• 2022

In this paper, we discuss the relative positioning of Wh-related English prepositions in a Wh-interrogative construction within the Optimality Theory [1-2]. By employing the two key constraints such as ^*Prep-Str and Align which are developed for the positioning of Wh-related prepositions from Romance languages such as French and Italian [3] and for the positioning of Wh-related prepositions from the middle English prose from 1500 to 1900 [4-6], and by slightly modifying the constraint hierarchy of ^*Prep-STR >>Align into ^**PrepSTR <<>>Align, Choi argues that his new theory can properly explain the unique behaviors of English Whrelated prepositions being able to take two 'optional' operations such as pied-piping and stranding to find legitimate landing sites in a Wh-interrogative construction [7]. However, this new analysis again reveals the following critical problems: (1) Unlike the 'light' English Wh-related prepositions which can two optional operations for legitimate landing sites in a Wh-interrogative construction, 'heavy' Wh-related English prepositions are not allowed to have such two options: they take just one option of pied-piping only. Thus, (2) his argumentation based on the existing constraints and the modified constraint hierarchy is neither general enough nor proper to explain the issue of the relative positioning for all English Wh-related preposition cases. To include such exceptional syntactic property of the 'heavy' preposition cases within the Optimality Theory, we suggest a new constraint of ^*HPrep-STR ranked at the highest position of the constraint hierarchy to disallow a 'heavy' or multi-syllabic Wh-related English preposition to stay alone at the end of a sentence. The new final hierarchy of constraints we suggest to explain the exceptional positioning of 'heavy' Wh-related prepositions together with the other 'light' Wh-related prepositions in English Wh-interrogative construction will be as follows: ^*HPrep-STR>>Align<<>>^*Prep-STR.

• International Journal of Advanced Culture Technology
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• v.6 no.4
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• pp.58-64
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• 2018

The Extraposition phenomenon in English has been analyzed mainly through two approaches: a derivational approach under the Principles & Parameters framework (P&P) and a representational approach under the early Minimalist framework (MP). The first one tries to understand the phenomenon as a result of the movement of a Big Subject first to the end of a sentence which is then followed by the insertion of an expletive 'it' to the empty Subject position. On the other hand, the second one tries to understand it by way of assuming a Big Subject originally base-generated at the end of a sentence which is followed by the insertion of an expletive 'it' to the empty Subject position. The two approaches, however, are not free from theoretical defects at all: the full derivational approach was under controversy in terms of (1) the failure of the Binding Theory and (2) its inability to suggest anything about the marginal reading issue. On the while, the representational approach has been argued (1) to violate the thematic hierarchy that should be kept in D-structure, and (2) to be also unable to suggest the slightest difference in marginal reading issue as the first one. In this paper I focus mainly on analyzing the 'It'-Extraposition phenomenon in the Optimality Theory. I will show that by way of (i) some newly developed constraints such as Subj., and AHSubj. and (ii) a constraint hierarchy of Subj.>>AHSubj., the controversies of 'It-Extraposition' such as (1) the analysis of construction and (2) the very closely related issue of 'marginal reading issue' can be explained properly.