• Korean Journal of Mathematics
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• v.4 no.1
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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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• 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.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.5 no.2
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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.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.11 no.4
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• pp.91-102
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• 1991

Traditionally, a dynamic programming(DP) technique has been used to the multireservoir control system. The algorithm has inherent problem to increase computational requirements exponentially due to discretization of variables and expanding the dimension of the system. To solve this problem, this paper describes transforming the optimal control system into a quadratic programming(QP), using Laguerre polynomials(LP) and its properties. The objective function of the proposed QP is independent of time variable. The solution of the QP is obtained by nonlinear programming(NLP) using augmented Lagrangian multiplier method. The numerical experiment shows that the water level of reservoirs is higher than Lee's and the evaluated benefit value is about the same as other researcher's.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.38A no.6
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• pp.459-464
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• 2013

In this paper, we introduce a modulation code design problem where best selection of two-dimensional codewords are determined to reduce two-dimensional (2D) intersymbol interference (ISI) and interpage interference (IPI). Codeword selection problem is formulated as a quadratic integer programming model that minimizes intra- and inter-symbol differences subject to uniform symbol usage and minimal Hamming distance violations. Second integer programming model detects the occurrence of isolated pixel pattern in the selected codewords. The proposed models are applied to 4-level and 2-level 6/8 codes.

• The Transactions of the Korean Institute of Electrical Engineers A
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• v.50 no.12
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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.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.27 no.3
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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.

• Journal of the Korean Operations Research and Management Science Society
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• v.10 no.1
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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.

• Journal of Drive and Control
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• v.14 no.4
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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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• v.26 no.1_2
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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.