• Journal of applied mathematics & informatics
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• 제28권5_6호
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• pp.1535-1544
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• 2010

Sufficient optimality conditions for a class of generalized non-differentiable fractional optimization programming problems are established. Moreover, we prove the weak and strong duality theorems under (V, $\rho$)-invexity assumption.

• East Asian mathematical journal
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• 제35권3호
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• pp.289-296
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• 2019

We establish necessary and sufficient optimality conditions for a nonsmooth fractional robust optimization programming problems. Moreover, we prove the weak and strong duality theorems under (V, ${\rho}$)-invexity assumption.

• 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.

• 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.

• 대한수학회논문집
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• 제19권1호
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• pp.179-196
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• 2004

Mond-Weir type duals for multiobjective variational problems are formulated. Under generalized vector variational type I invexity assumptions on the functions involved, sufficient optimality conditions, weak and strong duality theorems are proved efficient and properly efficient solutions of the primal and dual problems.

• 대한수학회지
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• 제41권5호
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• pp.821-864
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• 2004

Both parametric and parameter-free necessary and sufficient optimality conditions are established for a class of nondiffer-entiable nonconvex optimal control problems with generalized fractional objective functions, linear dynamics, and nonlinear inequality constraints on both the state and control variables. Based on these optimality results, ten Wolfe-type parametric and parameter-free duality models are formulated and weak, strong, and strict converse duality theorems are proved. These duality results contain, as special cases, similar results for minmax fractional optimal control problems involving square roots of positive semi definite quadratic forms, and for optimal control problems with fractional, discrete max, and conventional objective functions, which are particular cases of the main problem considered in this paper. The duality models presented here contain various extensions of a number of existing duality formulations for convex control problems, and subsume continuous-time generalizations of a great variety of similar dual problems investigated previously in the area of finite-dimensional nonlinear programming.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제13권2호
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• pp.101-108
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• 2009

In this paper, we introduce generalized multiobjective fractional programming problem with two kinds of inequality constraints. Kuhn-Tucker sufficient and necessary optimality conditions are given. We formulate a generalized multiobjective dual problem and establish weak and strong duality theorems for an efficient solution under generalized convexity conditions.

• 응용통계연구
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• 제34권2호
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• pp.279-293
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• 2021

본 논문은 선형 회귀모형에서 벌점 추정량의 신의 성질에 대한 충분조건을 구성하는 방법을 소개하였다. 신의 추정량, 벌점 추정량, 신의 벌점 추정량, 신의 성질을 명확히 정의하였으며 이를 바탕으로 신의 성질에 대한 최적조건과 최적조건에 대한 충분조건을 구성하는 방법을 대부분의 벌점함수에 적용 가능하도록 하나의 통합된 원리로 소개하였다. 추가로 신의 성질에 대한 이해를 돕기 위해 간단한 예제와 함께 가상실험 결과를 첨부하였다.

• Journal of applied mathematics & informatics
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• 제27권1_2호
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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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• 제30권1_2호
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• pp.111-125
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• 2012

In this paper, we introduce new classes of generalized convex n-set functions called $d$-weak strictly pseudo-quasi type-I univex, $d$-strong pseudo-quasi type-I univex and $d$-weak strictly pseudo type-I univex functions and focus our study on multiobjective subset programming problem. Sufficient optimality conditions are obtained under the assumptions of aforesaid functions. Duality results are also established for Mond-Weir and general Mond-Weir type dual problems in which the involved functions satisfy appropriate generalized $d$-type-I univexity conditions.