• Journal of applied mathematics & informatics
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• v.15 no.1_2
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• pp.185-200
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• 2004

A stochastic optimal LQR control problem under some integral quadratic (IQ) constraints is studied, with cross terms in both the cost and the constraint functionals, allowing all the control weighting matrices being indefinite. Sufficient conditions for the well-posedness of this problem are given. When these conditions are satisfied, the optimal control is explicitly derived via dual theory.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.13 no.2
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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.

• Structural Engineering and Mechanics
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• v.26 no.1
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• pp.15-30
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• 2007

In the paper, one focuses on the problem of duality in non-linear programming, applied to the solution of no-tension problems by means of Limit Analysis (LA) theorems for Not Resisting Tension (NRT) models. In details, one demonstrates that, starting from the application of the duality theory to the non-linear program defined by the static theorem approach for a discrete NRT model, this procedure results in the definition of a dual problem that has a significant physical meaning: the formulation of the kinematic theorem.

• East Asian mathematical journal
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• v.32 no.5
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• pp.635-639
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• 2016

In this paper, we prove a sufficient optimality theorems for the problem(FP) under(V, ${\rho}$)-invexity assumption. And we give Mond-Weir type dual problem and proved weak and strong duality theorem under (V, ${\rho}$)-invexity

• Journal of applied mathematics & informatics
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• v.12 no.1_2
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• pp.211-218
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• 2003

Let H be a Hilbert space, X be a real Banach space, A : H \longrightarrow X be an operator with D(A) dense in H, G： H \longrightarrow H be positive definite, $\chi$ $\in$ D(A) and b $\in$ H. Consider the quadratic programming problem: QP： Minimize $\frac{1}{2}$〈p, $\chi$〉 + 〈$\chi$, G$\chi$〉 subject to A$\chi$= b In this paper, we obtain an explicit solution to the above problem using generalized inverses.

• Proceedings of the Korea Society for Simulation Conference
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• 1998.03a
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• pp.11-16
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• 1998

The classical algorithm for solving liner network flow problems are primal cost improvement method, including simplex method, which iteratively improve the primal cost by moving flow around simple cycles, which iteratively improve the dual cost by changing the prices of a subset of nodes by equal amounts. Typical iteration/shortest path algorithm is used to improve flow problem of liner network structure. In this paper we stdudied about the implemental method of shortest path which is a practical computational aspects. This method can minimize the best neighbor node and also implement the typical iteration which is $\varepsilon$-CS satisfaction using the auction algorithm of linear network flow problem

• The Transactions of the Korean Institute of Electrical Engineers
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• v.33 no.6
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• pp.241-246
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• 1984

The power system scheduling process is formulated as an optimization problem with linear inequality constraints. AC Loadflow method is used for the problem solution and line losses are considered. The constraints under consiceration are generator power limits, load schedding limits and line capacity limits. In solving the objective function the Dual Relaxation method is adopted. Tests indicate that the method is practical for real time applications.

• Journal of KIISE:Databases
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• v.28 no.3
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• pp.357-372
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• 2001

In this paper, we present the concept of generalization in constructing windows for subsequence matching and propose a new subsequence matching method. GeneralMatch, based on the generalization. The earlier work of Faloutsos et al.(FRM in short) causes a lot of false alarms due to lack of the point-filtering effect. DualMatch, which has been proposed by the authors, improves performance significantly over FRM by exploiting the point filtering effect, but it has the problem of having a smaller maximum window size (half that FRM) given the minimum query length. GeneralMatch, an improvement of DualMatch, offers advantages of both methods: it can use large windows like FRM and, at the same time, can exploit the point-filtering effect like DualMatch. GeneralMatch divides data sequences into J-sliding windows (generalized sliding windows) and the query sequence into J-disjoint windows (generalized disjoint windows). We formally prove that our GeneralMatch is correct, i.e., it incurs no false dismissal. We also prove that, given the minimum query length, there is a maximum bound of the window size to guarantee correctness of GeneralMatch. We then propose a method of determining the value of J that minimizes the number of page accesses, Experimental results for real stock data show that, for low selectivities ($10^{-6}~10^{-4}$), GeneralMatch improves performance by 114% over DualMatch and by 998% iver FRM on the average; for high selectivities ($10^{-6}~10^{-4}$), by 46% over DualMatch and by 65% over FRM on the average.

• Journal of the Korean Operations Research and Management Science Society
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• v.12 no.1
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• pp.34-44
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• 1987

The general vehicle routing problem has been studied by many researchers such as Christofides, et al. and Laporte, et al., but only limited effort has been devoted to developing the optimal algorithms. The purpose of this paper is to develop a branch and bound algorithm which determines the optimal vechicle routes and the optimal number of vehicles concurrenetly for the asymmetrical vehicle routing problem. In order to enhance the efficiency, this algorithm emphasizes the followings ; First, an efficient primal-dual approach is developed to solve subproblems which are called the specialized transportation problem, formed by relaxing the illegal subtour constraints from the vehicle routing problem, second, an improved branching scheme is developed to reduce the number of candidate subproblems by adequate utilization of vehicle capacity restrictions.

• Journal of applied mathematics & informatics
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• v.13 no.1_2
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• pp.85-97
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• 2003

An indefinite stochastic linear-quadratic(LQ) optimal control problem with cross term over an infinite time horizon is studied, allowing the weighting matrices to be indefinite. A systematic approach to the problem based on semidefinite programming (SDP) and .elated duality analysis is developed. Several implication relations among the SDP complementary duality, the existence of the solution to the generalized Riccati equation and the optimality of LQ problem are discussed. Based on these relations, a numerical procedure that provides a thorough treatment of the LQ problem via primal-dual SDP is given: it identifies a stabilizing optimal feedback control or determines the problem has no optimal solution. An example is provided to illustrate the results obtained.