• Journal of the military operations research society of Korea
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• v.9 no.1
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• pp.51-61
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• 1983

Lagrangian relaxation is used to the problem of scheduling jobs on unrelated parallel processors with the objective of minimizing makespan. The implicit condition for optimality is drawn out explicitly in order to apply the subgradient algorithm. To obtain the optimal solution, branch-and-bound-search method is devised. In the search, the special structure of the problem is exploited effectively, Some computational experiences with the algorithm are presented, and comparisons are made with the Land and Doig method.

• Proceedings of the Korean Operations and Management Science Society Conference
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• 2003.05a
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• pp.129-136
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• 2003

설비입지문제는 고객에게 좋은 서비스를 제공하면서 전체 비용을 최소화하는 의사결정을 요구한다. 본 논문은 제한된 총 투자 비용 하에서 최대의 서비스 수준을 달성하기 위하여 고정비를 가지는 설비의 입지를 결정하는 문제에 관한 것이다. 이 문제에 대해 수리 모형을 제시하고, 라그랑지안 기법을 이용한 발견적 기법을 통하여 해를 구하였다. 문제의 상한(Upper Bound)은 서브그래디언트(Subgradient) 최적화 기법을 사용하여 구하였고, 하한(Lower Bound)을 구하기 위하여 커팅(Cutting) 알고리즘이라는 새로운 기법을 개발하여 적용하였다. 임의로 생성된 데이터를 이용하여 비용과 커버 가능거리라는 두 가지 관점에서 실험을 하고 제안된 알고리즘의 성능을 비교 분석하였다.

• Journal of the Korean Institute of Telematics and Electronics S
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• v.34S no.9
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• pp.13-22
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• 1997

In this paper, we supposed allocating the number of redundancies as the model of 0-1 knapsack problem and formulated the problem to maximize the systems reliability for a mission length. The formulated problem reduced the problem size using the modified branch and bound algorithm by Lagrangian relaxation. The subgradient method can optimize the set of solution. To verify the proposed method, we presented the improved resutls of the systems composed of two and ten component groups as the commparison of those in other papers.

• Journal of Communications and Networks
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• v.12 no.3
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• pp.246-252
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• 2010

A binary linear integer program is formulated for the problem of expanding the capacity of a fiber optic network and routing the traffic to deliver new interactive multimedia services. A two-phase Lagrangian dual search procedure and a Lagrangian heuristic are developed. Computational results show superior performance of the two-phase subgradient optimization compared with the conventional one-phase approach.

• Journal of applied mathematics & informatics
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• v.23 no.1_2
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• pp.361-367
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• 2007

In this paper we propose an implementable method for solving a nonsmooth convex optimization problem by combining Moreau-Yosida regularization, bundle and quasi-Newton ideas. The method we propose makes use of approximate subgradients of the objective function, which makes the method easier to implement. We also prove the convergence of the proposed method under some additional assumptions.

• Journal of applied mathematics & informatics
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• v.28 no.5_6
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• pp.1239-1248
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• 2010

In this paper, an implementable BFGS bundle algorithm for solving a nonsmooth convex optimization problem is presented. The typical method minimizes an approximate Moreau-Yosida regularization using a BFGS algorithm with inexact function and the approximate gradient values which are generated by a finite inner bundle algorithm. The approximate subgradient of the objective function is used in the algorithm, which can make the algorithm easier to implement. The convergence property of the algorithm is proved under some additional assumptions.

• Bulletin of the Korean Mathematical Society
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• v.59 no.4
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• pp.1019-1044
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• 2022

In this paper, we propose new algorithms for solving equilibrium and multivalued variational inequality problems in a real Hilbert space. The first algorithm for equilibrium problems uses only one approximate projection at each iteration to generate an iteration sequence converging strongly to a solution of the problem underlining the bifunction is pseudomonotone. On the basis of the proposed algorithm for the equilibrium problems, we introduce a new algorithm for solving multivalued variational inequality problems. Some fundamental experiments are given to illustrate our algorithms as well as to compare them with other algorithms.

• Journal of the Institute of Convergence Signal Processing
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• v.4 no.1
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• pp.27-35
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• 2003

Because of the lack of translation invariance of wavelet basis, traditional wavelet thresholding denoising leads to pseudo-Gibbs phenomena in the vicinity of discontinuities of signal. In this paper, in order to reduce the pseudo-Gibbs phenomena, wavelet coefficients are thresholded and reconstruction algorithm is implemented through minimizing the total variation of denoising signal using subgradient descent algorithm. Most of experiments were performed under the non-real-time and real-time environments. In the case of non-real-time experiments, the algorithm that this paper proposes was found more effective than that of wavelet hard thresholding denoising by 2.794㏈(SNR) based on the signal to noise ratio. And lots of pseudo-Gibbs phenomena was removed visually in the vicinity of discontinuities. In the case of real-time experiments, the number of iteration was restricted to 60 times considering the performance time. It took 0.49 seconds and most of the pseudo-Gibbs phenomena were also removed.

• Journal of the Korean Operations Research and Management Science Society
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• v.23 no.2
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• pp.47-65
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• 1998

We consider a multiperiod capacity planning problem for determining a mix of flexible and dedicated capacities under budget restriction. These capacities are controlled by purchasing flexible machines and/or new dedicated machines and disposing old dedicated machines. Acquisition and replacement schedules are determined and operations are assigned to the flexible or dedicated machines for the objective of minimizing the sum of discounted costs of acquisition and operation of flexible machines, new dedicated machines, and old dedicated machines. In this research, the Problem is formulated as a mixed integer linear Program and solved by a Lagrangian relaxation approach. A subgradient optimization method is employed to obtain lower bounds and a multiplier adjustment method is devised to improve the bounds. We develop a linear programming based Lagrangian heuristic algorithm to find a good feasible solution of the original problem. Results of tests on randomly generated test problems show that the algorithm gives relatively good solutions in a reasonable amount of computation time.

• Journal of the Korean Operations Research and Management Science Society
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• v.18 no.3
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• pp.13-34
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• 1993

By operating on many part of a software system concurrently, the parallel processing computers may provide several orders of magnitude more computing power than traditional serial computers. If the Lagrangean approximation procedure is applied to a large scale manufacturing problem which is decomposable into many subproblems, the procedure is a perfect candidate for parallel processing. By distributing Lagrangean subproblems for given multiplier to multiple processors, concurrently running processors and modifying Lagrangean multipliers at the end of each iteration of a subgradient method,a parallel processing of a Lagrangean approximation procedure may provide a significant speedup. This purpose of this research is to investigate the potential of the parallelized Lagrangean approximation procedure (PLAP) for certain combinational optimization problems in manufacturing systems. The framework of a Plap is proposed for some combinatorial manufacturing problems which are decomposable into well-structured subproblems. The synchronous PLAP for the multistage dynamic lot-sizing problem is implemented on a parallel computer Alliant FX/4 and its computational experience is reported as a promising application of vector-concurrent computing.