• Journal of applied mathematics & informatics
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• 제16권1_2호
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• pp.125-142
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• 2004

We analyze the convergence properties of Powell's UOBYQA method. A distinguished feature of the method is its use of two trust region radii. We first study the convergence of the method when the objective function is quadratic. We then prove that it is globally convergent for general objective functions when the second trust region radius p converges to zero. This gives a justification for the use of p as a stopping criterion. Finally, we show that a variant of this method is superlinearly convergent when the objective function is strictly convex at the solution.

• Journal of the Korean Data and Information Science Society
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• 제21권2호
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• pp.291-296
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• 2010

In this paper, we consider a versatile test based on percentile tests. The versatile test may be useful when the underlying distributions are unknown or quite different types. We consider two kinds of combining functions for the percentile statistics, the quadratic and summing forms and obtain the limiting distributions under the null hypothesis. Then we illustrate our procedure with an example. Finally we discuss some interesting features of the test as concluding remarks.

• Journal of the Chungcheong Mathematical Society
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• 제24권4호
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• pp.919-920
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• 2011

For two even unimodular positive definite integral quadratic forms A[X], B[X] in n-variables, J. K. Koo [1, Theorem 1] showed that ${\theta}_A(\tau)/{\theta}_B(\tau)$ is a rational function of J, satisfying a certain condition. Where ${\theta}_A(\tau)$ and ${\theta}_B(\tau)$ are theta series related to A[X] and B[X], respectively, and J is the classical modular invariant. In this paper we give a simple proof of Theorem 1 of [1].

• Journal of Integrative Natural Science
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• 제14권3호
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• pp.73-77
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• 2021

Robust design is an approach to reduce the performance variation of mutiple responses in products and processes. In fact, in many experimental designs require the simultaneous optimization of multiple responses. In this paper, we propose how to simultaneously optimize multiple responses for robust design when data are collected from a combined array. The proposed method is based on the quadratic loss function. An example is illustrated to show the proposed method.

• Journal of the Korean Mathematical Society
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• 제41권5호
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• pp.821-864
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• 2004

Both parametric and parameter-free necessary and sufficient optimality conditions are established for a class of nondiffer-entiable nonconvex optimal control problems with generalized fractional objective functions, linear dynamics, and nonlinear inequality constraints on both the state and control variables. Based on these optimality results, ten Wolfe-type parametric and parameter-free duality models are formulated and weak, strong, and strict converse duality theorems are proved. These duality results contain, as special cases, similar results for minmax fractional optimal control problems involving square roots of positive semi definite quadratic forms, and for optimal control problems with fractional, discrete max, and conventional objective functions, which are particular cases of the main problem considered in this paper. The duality models presented here contain various extensions of a number of existing duality formulations for convex control problems, and subsume continuous-time generalizations of a great variety of similar dual problems investigated previously in the area of finite-dimensional nonlinear programming.

• The Transactions of the Korean Institute of Electrical Engineers
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• 제40권3호
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• pp.243-249
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• 1991

Adaptive mesh refinement scheme is incorporated with the boundary element analysis in order to get accurate solution with relatively fewer unnowns for magnetostatic field analysis. A new andsimple posteriori local error estimate is also presented. The local error is defined as an integraktion over the element of the difference between solutions from quadratic interpolation functions and linear interpolation functions and is used as the criterion for mesh refinement. Case study with a singular point reveals that adaptive meshes are more efficient in accuracy of solutions than uniform meshs generated by dividing al the elements evenly. The adaptive meshes give much better rate of convergence in global errors than the uniform meshes.

• Journal of Advanced Research in Ocean Engineering
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• 제2권2호
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• pp.81-85
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• 2016

Nonlinear wave loads can lead to resonant responses of offshore structures in sum or difference frequencies. In this study, the roll motion of an FPSO with a low natural frequency is simulated in the time domain. To generate the time signals of wave loads, the quadratic transfer functions of the second-order excitations are calculated in the frequency domain. The equations of motions based on the time memory functions are used to evaluate the roll responses in irregular waves. The roll damping in empirical form is accounted for in the simulation.

• Proceedings of the KIEE Conference
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• 대한전기학회 2006년도 심포지엄 논문집 정보 및 제어부문
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• pp.273-275
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• 2006

In this paper, we introduce a new design of fuzzy neural networks using input-output data information of target system. The proposed fuzzy neural networks is constructed by input-output data information and used the center of data distance by HCM clustering to obtain the characteristics of data. A membership function is defined by HCM clustering and is applied input-output dat included each rule to conclusion polynomial functions. We use triangular membership functions and simplified fuzzy inference, linear fuzzy inference, and modified quadratic fuzzy inference in conclusion. In the networks learning, back propagation algorithm of network is used to update the parameters of the network. The proposed model is evaluated with benchmark data.

• Bulletin of the Korean Mathematical Society
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• 제54권3호
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• pp.1037-1067
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• 2017

Motzkin and Straus established a close connection between the maximum clique problem and a solution (namely graph-Lagrangian) to the maximum value of a class of homogeneous quadratic multilinear functions over the standard simplex of the Euclidean space in 1965. This connection and its extensions were successfully employed in optimization to provide heuristics for the maximum clique problem in graphs. It is useful in practice if similar results hold for hypergraphs. In this paper, we develop a homogeneous multilinear function based on the structure of hypergraphs and their complement hypergraphs. Its maximum value generalizes the graph-Lagrangian. Specifically, we establish a connection between the clique number and the generalized graph-Lagrangian of 3-uniform graphs, which supports the conjecture posed in this paper.

• International Journal of Air-Conditioning and Refrigeration
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• 제6권
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• pp.14-26
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• 1998

This paper deals with approximate analytical solutions for the two-region one-dimensional model describing the charging process of stratified thermal storage tanks at variable inlet temperature with momentum-induced mixing. An arbitrarily increasing inlet temperature is decomposed into inherent step changes and intervals of continuous change. Each continuous interval is approximated as a finite number of piecewise linear functions, which admits an analytical solution for perfectly mixed region. Using the Laplace transform, the temperature profiles in plug flow region with both the semi-infinite and adiabatic ends are successfully derived in terms of well-defined functions. The effect of end condition on the solution proves to be negligible under the practical operating conditions. For a Quadratic variation of inlet temperature, the approximate solution employing a moderate number of pieces agrees excellently with the exact solution.