• Journal of Korean Society of Industrial and Systems Engineering
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• v.9 no.13
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• pp.45-50
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• 1986

본 연구에서 고찰한 surrogate relaxation은 Lagrangian relaxation 방법과는 달리 제약식들을 선형조합으로 묶어 문제를 푼다. 수리계획 분계가 convexity를 만족하지 못하는 경우에는 Lagrangian의 경우와 마찬가지로 surrogate gap이 발생한다. Lagrangian 쌍대이론을 토대로 surrogate optimality condition을 알아보고 수리계획법의 특별 형태인 정수선형계획법에 적용해 보았다. 일반적으로 surrogate gap은 Lagrangian gap 보다 작기 때문에 좀더 근사하게 원 문제의 최적 목적 함수값에 접근할 수 있다. 따라서 branch and bound 알고리즘을 개발할 때 중요한 정보를 제공하는 것이다.

• 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 Communications and Networks
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• v.11 no.2
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• pp.166-174
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• 2009

In this paper, a distributed power and end-to-end rate control algorithm is proposed in the presence of licensed users. By Lagrangian duality theory, the optimal power and rate control solution is given for the unlicensed users while satisfying the interference temperature limits to licensed users. It is obtained that transmitting with either 0 or the maximum node power is the optimal scheme. The synchronous and asynchronous distributed algorithms are proposed to be implemented at the nodes and links. The convergence of the proposed algorithms are proved. Finally, further discussion on the utility-based fairness is provided for the proposed algorithms. Numerical results show that the proposed algorithm can limit the interference to licensed user under a predefined threshold.