• Korean Journal of Mathematics
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• 제4권1호
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• pp.7-16
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• 1996

The optimization problems with quadratic constraints often appear in various fields such as network flows and computer tomography. In this paper, we propose an algorithm for solving those problems and prove the convergence of the proposed algorithm.

• Journal of applied mathematics & informatics
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• 제12권1_2호
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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.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제5권2호
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• pp.137-147
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• 2001

Nonconvex Quadratic Optimization Problems (QOP) are solved approximately by SDP (semidefinite programming) relaxation and SOCP (second order cone programmming) relaxation. Nonconvex QOPs with special structures can be solved exactly by SDP and SOCP. We propose a method to formulate general nonconvex QOPs into the special form of the QOP, which can provide a way to find more accurate solutions. Numerical results are shown to illustrate advantages of the proposed method.

• 대한토목학회논문집
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• 제11권4호
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• pp.91-102
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• 1991

저수지군을 최적으로 운영하려고 할때 일반적으로 동적계획법을 이용하는데 저수지 수의 증가와 변수의 이산화에 따라 계산 용량이 지수적으로 팽창하는 결점을 내포하고 있다. 이 문제를 해결하기 위해서 본 논문에서는 저수지 시스템 변수가 LP(Laguerre Polynomial)로 표현된 새로운 모형 개발을 시도하였다. 새로운 계획모형은 QP(Quadratic Programming) 형태이다. 이 모형의 해는 확장 라그란지안 곱수 방법(Augmented Lagrangian Multiplier Method)의 비선형계획법에 의해서 QP해를 구하였다. 그 결과 저수 수준은 기존의 결과보다 높게 유지하려는 경향을 보였으며, 평가된 편익 값은 다른 방법들과 비슷한 값이었다.

• 한국통신학회논문지
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• 제38A권6호
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• pp.459-464
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• 2013

본 연구에서는 이차원 인접 심볼간 간섭(2D ISI) 및 인접 페이지간 간섭 (IPI)을 줄이는 홀로그래픽 저장장치를 위한 이차원 변조부호를 선택하는 문제를 고려한다. 변조부호 선택문제는 목적함수로 코드내부와 코드 상호간 인접심볼값의 차이를 최소화하고, 제약식으로는 사용된 심볼의 분포가 균등하며, 최소 해밍거리 조건이 주어진 이차정수계획법 모형으로 수식화되었다. 선택된 코드워드에서 고립된 픽셀의 발생여부를 검색하는 모형은 정수계획법 모형으로 수식화되었다. 제안된 모형들은 4-레벨 6/8 코드 및 2-레벨 6/8 코드에 적용되어 성능을 계산하였다.

• 대한전기학회논문지:전력기술부문A
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• 제50권12호
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• pp.584-590
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• 2001

This paper presents a windows program package for solving security constrained OPF in interconnected Power systems, which is based on the combined application of evolutionary programming(EP) and sequential quadratic programming(SQP). The objective functions are the minimization of generation fuel costs and system power losses. The control variables are the active power of the generating units, the voltage magnitude of the generator, transformer tap settings and SYC setting. The state variables are the bus voltage magnitude, the reactive power of the generating unit, line flows and the tie line flow In OPF considering security, the outages are selected by contingency ranking method. The resulting optimal operating point has to be feasible after outages such as any single line outage(respect of voltage magnitude, reactive power generation and power flow limits). The OPF package proposed is applied to IEEE 14 buses and 10 machines 39 buses model system.

• 산업경영시스템학회지
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• 제27권3호
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• pp.7-13
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• 2004

In this paper, machine cell formation problem is discussed. To reflect precisely actual manufacturing situations such as routing sequences, production quantities, and machining (or operation) characteristics, a new network presentation (or the problem is proposed. It is formulated as a simple 0-1 quadratic programming model with linear constraints. Then, the model is converted into a 0-1 integer programming model using a variable transformation technique. Lastly, some computational results are presented.

• 한국경영과학회지
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• 제10권1호
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• pp.9-13
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• 1985

This paper develops a decomposition method for stochastic programming with a block diagonal structure. Here we assume that the right-hand side random vector of each subproblem is differente each other. We first, transform this problem into a master problem, and subproblems in a similar way to Dantizig-Wolfe's Decomposition Princeple, and then solve this master problem by solving subproblems. When we solve a subproblem, we first transform this subproblem to a Deterministic Equivalent Programming (DEF). The form of DEF depends on the type of the random vector of the subproblem. We found the subproblem with finite discrete random vector can be transformed into alinear programming, that with continuous random vector into a convex quadratic programming, and that with random vector of unknown distribution and known mean and variance into a convex nonlinear programming, but the master problem is always a linear programming.

• 드라이브 ㆍ 컨트롤
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• 제14권4호
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• pp.45-50
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• 2017

The gas spring is a hydropneumatic adjusting element, consisting of a pressure tube, a piston rod, a piston and a connection fitting. The gas spring is filled with compressed nitrogen within the cylinder. The filling pressure acts on both sides of the piston and because of area difference it produces an extension force. Therefore, a gas spring is similar in function compare to mechanical coil spring. Conversely, optimization is a process of finding the best set of parameters to reach a goal while not violating certain constraints. The AMESim software provides NLPQL (Nonlinear Programming by Quadratic Lagrangian) and GA (genetic algorithm) for optimization. The NLPQL method builds a quadratic approximation to the Lagrange function and linear approximations to all output constraints at each iteration, starting with the identity matrix for the Hessian of the Lagrangian, and gradually updating it using the BFGS method. On each iteration, a quadratic programming problem is solved to find an improved design until the final convergence to the optimum design. In this study, we conducted optimization design of the gas spring reaction force with NLPQL.

• Journal of applied mathematics & informatics
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• 제26권1_2호
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• pp.75-106
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• 2008

In this paper, we derive necessary optimality conditions for a continuous programming problem in which both objective and constraint functions contain support functions and is, therefore, nondifferentiable. It is shown that under generalized invexity of functionals, Karush-Kuhn-Tucker type optimality conditions for the continuous programming problem are also sufficient. Using these optimality conditions, we construct dual problems of both Wolfe and Mond-Weir types and validate appropriate duality theorems under invexity and generalized invexity. A mixed type dual is also proposed and duality results are validated under generalized invexity. A special case which often occurs in mathematical programming is that in which the support function is the square root of a positive semidefinite quadratic form. Further, it is also pointed out that our results can be considered as dynamic generalizations of those of (static) nonlinear programming with support functions recently incorporated in the literature.