• Journal of the Korean Mathematical Society
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• v.44 no.4
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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.

• Communications of the Korean Mathematical Society
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• v.25 no.1
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• pp.139-147
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• 2010

A generalized nondifferentiable fractional optimization problem (GFP), which consists of a maximum objective function defined by finite fractional functions with differentiable functions and support functions, and a constraint set defined by differentiable functions, is considered. Recently, Kim et al. [Journal of Optimization Theory and Applications 129 (2006), no. 1, 131-146] proved optimality theorems and duality theorems for a nondifferentiable multiobjective fractional programming problem (MFP), which consists of a vector-valued function whose components are fractional functions with differentiable functions and support functions, and a constraint set defined by differentiable functions. In fact if $\overline{x}$ is a solution of (GFP), then $\overline{x}$ is a weakly efficient solution of (MFP), but the converse may not be true. So, it seems to be not trivial that we apply the approach of Kim et al. to (GFP). However, modifying their approach, we obtain optimality conditions and duality results for (GFP).

• 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.

• Management Science and Financial Engineering
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• v.7 no.1
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• pp.41-56
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• 2001

This linear fractional - quadratic bilevel programming problem, in which the leader's objective function is a linear fractional function and the follower's objective function is a quadratic function, is studied in this paper. The leader's and the follower's variables are related by linear constraints. The derivations of the optimality conditions are based on Kuhn-Tucker conditions and the duality theory. It is also shown that the original linear fractional - quadratic bilevel programming problem can be solved by solving a standard linear fractional program and the optimal solution of the original problem can be achieved at one of the extreme point of a convex polyhedral formed by the new feasible region. The algorithm is illustrated with the help of an example.

• Journal of applied mathematics & informatics
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• v.30 no.1_2
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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.

• Journal of the Korean Mathematical Society
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• v.47 no.1
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• pp.17-28
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• 2010

In this paper we deal with linear chance-constrained optimization problems, a class of problems which naturally arise in practical applications in finance, engineering, transportation and scheduling, where decisions are made in presence of uncertainty. After giving the deterministic equivalent formulation of a linear chance-constrained optimization problem we construct a conjugate dual problem to it. Then we provide for this primal-dual pair weak sufficient conditions which ensure strong duality. In this way we generalize some results recently given in the literature. We also apply the general duality scheme to a portfolio optimization problem, a fact that allows us to derive necessary and sufficient optimality conditions for it.

• 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 Korean Institute of Industrial Engineers
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• v.41 no.3
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• pp.324-329
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• 2015

Though the supplier diversification is considered as a vital tool to mitigate the risk due to supply chain disruptions, there are results which show the optimality of the sole sourcing. This paper further generalizes the results to show that the sole sourcing is optimal under very mild conditions. Discussion on why the sole sourcing is optimal is given with the insight on the value of supplier diversification.

• East Asian mathematical journal
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• v.9 no.2
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• pp.353-363
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• 1993

• Korean Management Science Review
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• v.5 no.1
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• pp.56-70
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• 1988

In this study, We reviewed the solution methods (for the heuristic and optimization method) for the single-item dynamic lot-sizing problem, and improved the efficiency (speed and optimality) of the conventional heuristic method by utilizing the inventory decomposition property. The iventory decomposition property decomposes the given original problem into several independent subproblems without violating the optimality conditions. Then we solve each decomposed subproblems by using the conventional heuristics such as LTC, LUC, Silver-Meal etc. For testing the efficiency of the proposed decomposition method, we adopted the data sets given in Kaimann, Berry and Silver-Meal. The computational results show that the suggested problem solving framework results in some promising effects on the computation time and the degree of optimality.