• Journal of the Korean Operations Research and Management Science Society
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• v.17 no.1
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• pp.3-16
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• 1992

We present a modified Tank and Hopfield's neural network model for solving Linear Programming problems. We have found the fact that the Tank and Hopfield's neural circuit for solving Linear Programming problems has some difficulties in guaranteeing convergence, and obtaining both the primal and dual optimum solutions from the output of the circuit. We have identified the exact conditions in which the circuit stops at an interior point of the feasible region, and therefore fails to converge. Also, proper scaling of the problem parameters is required, in order to obtain a feasible solution from the circuit. Even after one was successful in getting a primal optimum solution, the output of the circuit must be processed further to obtain a dual optimum solution. The modified model being proposed in the paper is designed to overcome such difficulties. We describe the modified model and summarize our computational experiment.

• Journal of the Institute of Electronics and Information Engineers
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• v.50 no.8
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• pp.67-75
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• 2013

The advantages of the orthogonal frequency division multiplexing (OFDM) are high spectral efficiency, resiliency to RF interference, and lower multi-path distortion. To further utilize vast channel capacity of the multiuser OFDM, one has to find the efficient adaptive subchannel and bit allocation among users. In this paper, we compare the performance of the linear programming dual of the 0-1 integer programming formulation with the existing convex optimization approach for the optimal subchannel and bit allocation problem of the multiuser OFDM. Utilizing tight lower bound provided by the LP dual formulation, we develop a primal heurisitc algorithm based on the LP dual solution. The performance of the primal heuristic is compared with MAO, ESA heuristic solutions, and integer programming solution on MATLAB simulation on a system employing M-ary quadrature amplitude modulation (MQAM) assuming a frequency-selective channel consisting of three independent Rayleigh multi-paths.

• Journal of applied mathematics & informatics
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• v.15 no.1_2
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• pp.227-235
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• 2004

In this paper we consider the dual problems for multiobjective programming with generalized convex functions. We obtain the weak duality and the strong duality. At last, we give an equivalent relationship between saddle point and efficient solution in multiobjective programming.

• Journal of applied mathematics & informatics
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• v.11 no.1_2
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• pp.273-281
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• 2003

The purpose of this paper is to study the duality theorems in cone constrained multiobjective nonlinear programming for pseudo-invex objectives and quasi-invex constrains and the constraint cones are arbitrary closed convex ones and not necessarily the nonnegative orthants.

• Journal of the Korean Mathematical Society
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• v.48 no.1
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• pp.13-21
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• 2011

In this paper, a pair of Wolfe type nondifferentiable sec-ond order symmetric minimax mixed integer dual problems is formu-lated. Symmetric and self-duality theorems are established under $\eta_1$-bonvexity/$\eta_2$-boncavity assumptions. Several known results are obtained as special cases. Examples of such primal and dual problems are also given.

• Journal of applied mathematics & informatics
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• v.26 no.5_6
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• pp.819-837
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• 2008

A mixed type dual to the control problem in order to unify Wolfe and Mond-Weir type dual control problem is presented in various duality results are validated and the generalized invexity assumptions. It is pointed out that our results can be extended to the control problems with free boundary conditions. The duality results for nonlinear programming problems already existing in the literature are deduced as special cases of our results.

• Journal of applied mathematics & informatics
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• v.5 no.3
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• pp.797-804
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• 1998

A pair of multiobjective generalized symmetric dual non-linear programming problems and weak strong and converse dual-ity theorems for these problems are established under generalized $\rho-(\eta,0)$-invexity assumptions. Several known results are obtained as special cases.

• Journal of applied mathematics & informatics
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• v.13 no.1_2
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• pp.261-275
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• 2003

In this paper we study two stage problems of stochastic convex programming. Solving the problems is very hard. A L-shaped method for it is given. The implement of the algorithm is simple, so less computation work is needed. The result of computation shows that the algorithm is effective.

• Korean Management Science Review
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• v.16 no.1
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• pp.1-9
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• 1999

The purpose of this paper is to develope efficient techniques for implementing the dual simplex method. In this paper we proposed one artificial row technique to get an initial dual feasible basic solution, a dual steepest-edge method coupled with a dropping row selection rule, and an anti-degeneracy technique which resembles the EXPAND procedure for the primal simplex method. The efficiency of the above techniques is shown by experiments. Finally, the dual simplex method is shown to be superior to the primal simplex method when it is used in the integer programming.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 1998.06a
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• pp.506-511
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• 1998

In this paper we consider multiobjective linear programming problems with coefficients of the objective functions specified by possibility distributions. Possibly and necessarily efficient solution sets are defined as funny solution sets whose membership grades represent possibility and necessity degrees to which a feasible solution is efficient. Considering efficiency condition and its dual condition in ordinary multiobjective linear programming problem, we propose efficiency test methods based on an extreme ray generation method. Since the proposed methods can be put in the part of a bi-section method, we can develop calculation and methods of the degree of possible and necessary efficiency for feasible solutions.