• Journal of Korea Multimedia Society
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• v.9 no.12
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• pp.1636-1648
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• 2006

In this paper, we propose a new optimization approach to the rate control problem in a wired-cum-wireless network. A primal-dual interior-point(PDIP) algorithm is used to find the solution of the rate optimization problem. We show a comparison between the dual-based(DB) algorithm and PDIP algorithm for solving the rate control problem in the wired-cum-wireless network. The PDIP algorithm performs much better than the DB algorithm. The PDIP can be considered as an attractive method to solve the rate control problem in network. We also present a numerical example and simulation to illustrate our conclusions.

• Journal of the Korean Operations Research and Management Science Society
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• v.9 no.2
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• pp.3-8
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• 1984

This paper considers the intermediate warehouse location problem in a two stage distribution system where commodities are delivered from the given set of capacitated factories to customers via uncapacitated intermediate warehouses. In order to determine the subset of warehouses to open which minimizes the total distribution costs including the fixed costs associated with opening warehouses, the cross decomposition method for mixed integer programming recently developed by T.J. Van Roy is used. The cross decomposition unifies Benders decomposition and Lagrangean relaxation into a single framework that involves successive solutions to a primal subproblem and a dual subproblem. In our problem model, primal subproblem turns out to be a transshipment problem and dual subproblem turns out to be an intermediate warehouse location problem with uncapacitated factories.

• Journal of the Korean Operations Research and Management Science Society
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• v.25 no.1
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• pp.67-84
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• 2000

In this paper, we address a network design problem including the decision of hub facility locatiions which is typically found in a communicatio and a transportation network design studies. Due to the administrative and the geographical restrictions, it is common to assume that each user should be assigned to only one hub facility. To construct such a network, three types of network costs should be considered: the fixed costs of establishing the hubs and the arcs in the network, and the variable costs associated with transversing the network. The complex problem is formulated as a mixed IP embedding a multicommodity flow problem. Exploiting its special structure, a dual-based heuristic is then developed, which yields near-optimal design plans. The test results indicate that the heuristic is an effective way to solve this computationally complex problem.

• Korean Journal of Mathematics
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• v.30 no.3
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• pp.475-489
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• 2022

This paper focuses on a robust semi-infinite interval-valued optimization problem with uncertain inequality constraints (RSIIVP). By employing the concept of LU-optimal solution and Extended Mangasarian-Fromovitz Constraint Qualification (EMFCQ), necessary optimality conditions are established for (RSIIVP) and then sufficient optimality conditions for (RSIIVP) are derived, by using the tools of convexity. Moreover, a Wolfe type dual problem for (RSIIVP) is formulated and usual duality results are discussed between the primal (RSIIVP) and its dual (RSIWD) problem. The presented results are demonstrated by non-trivial examples.

• Bulletin of the Korean Mathematical Society
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• v.54 no.2
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• pp.647-654
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• 2017

Duality methods based on modified Lagrangian functional for solving a model crack problem is considered. Without additional assumptions of regularity of the solution of an initial problem duality ratio is established for initial and dual problem.

• Journal of applied mathematics & informatics
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• v.17 no.1_2_3
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• pp.351-360
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• 2005

This paper finds a new class of generalized convex function which satisfies the following properties: It's level set is $\eta$-convex set; Every feasible Kuhn-Tucker point is a global minimum; If Slater's constraint qualification holds, then every minimum point is Kuhn-Tucker point; Weak duality and strong duality hold between primal problem and it's Mond-Weir dual problem.

• Korean Journal of Logic
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• v.18 no.1
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• pp.83-133
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• 2015

In this paper, I pose a problem for Hitchcock's arguments for two concepts of effects that are intended to explicate double causal effects, and put forth a theory that is intended not just to meet the problem but also to accommodate Hitchcock's theory and Eells' theory both. First, I introduce an example of dual causal effects, and examine the accounts of Otte(1985) and Eells(1987) on how to explicate the dual effects. I show that their accounts of the dual effects help us understand the problem of dual effects and see how different it is for Cartwright(1979, 1989, 1995), Eells(1991, 1995), and Hitchcock(2001a) to meet the problem. Second, I introduce two concepts of effects on Hitchcock(2001a), that is, net effect and component effect that are allegedly analogous to two effects of structural equation model. Third, I reveal the significance of homogeneous subpopulation and causal interaction regarding the problem of dual effects while examining Cartwright's theory and Elles' theory. Fourth, I critically examine the two concepts of effects on Hitchcock and argue against Hitchcock's criticism of Eells' theory. Fifth, I take a moderator variable of structural equation model and a moderator effect into the probabilistic theory of causality, and formally generalize causal interaction due to the dual effects in terms of disjunctive relation and counterfactual conditionals. I expect my account of disjunctive relation and counterfactual conditionals to contribute not just to several problems the received theories of causal modelling confront but also to the structural equation models many people exploit as a promising statistical methodology.

• Communications for Statistical Applications and Methods
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• v.21 no.5
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• pp.395-409
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• 2014

Data limited, partial, or incomplete are known as an ill-posed problem. If the data with ill-posed problems are analyzed by traditional statistical methods, the results obviously are not reliable and lead to erroneous interpretations. To overcome these problems, we propose a dual generalized maximum entropy (dual GME) estimator for panel data regression models based on an unconstrained dual Lagrange multiplier method. Monte Carlo simulations for panel data regression models with exogeneity, endogeneity, or/and collinearity show that the dual GME estimator outperforms several other estimators such as using least squares and instruments even in small samples. We believe that our dual GME procedure developed for the panel data regression framework will be useful to analyze ill-posed and endogenous data sets.

• Journal of the Korean Mathematical Society
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• v.33 no.4
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• pp.777-791
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• 1996

Let $S(R^d)$ be the Schwartz space of infinitely differentiable functions on $R^d$ which vanish at $\infty$ and $S'(R^d)$ be its dual space. The theory of stochastic differential equations(SDEs) governing processes that takes values in the dual of countably Hilbertian nuclear space such as $S'(R^d)$ studied by many authors(e.g [M],[KM]). Let M be a martingale measure defined by Walsh[W], then M can be considered as a $S'(R^d)$-valued process in a certain condition i.e. M has a version of $S'(R^d)$-valued martingale process. (See [W] for detailed discussion)

• 제어로봇시스템학회:학술대회논문집
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• 1994.10a
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• pp.28-33
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• 1994

An optimal controller, e.g. LQG controller, may not be realistic in the sense that the required control power may not be achieved by existing actuators, and the measured output is not satisfactory. To be realistic, the controller should meet such constraints as sensor or actuator limitation, performance limit, etc. In this paper, the lnput/Output Variance Constrained (IOVC) control problem will be considered from the viewpoint of mathematical programming. A dual version shall be developed to solve the IOVC control problem, whose objective is to find a stabilizing control law attaining a minimum value of a quadratic cost function subject to the inequality constraint on each input and output variance for a stabilizable and detectable plant. One approach to the constrained optimization problem is to use the Kuhn-Tucker necessary conditions for the optimality and to seek an optimal point by an iterative algorithm. However, since the algorithm uses only the necessary conditions, the convergent point may not be optimal solution. Our algorithm will guarantee a sufficiency.