• Korean Journal of Mathematics
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• v.7 no.2
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• pp.207-213
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• 1999

In this paper we estimate a lower bound of the Banach-Mazur distance between a finite dimensional nonlocally convex space and its Banach envelope space by investigating the properties of the nonlocally convex space and the projection constant which are obtained by factoring the identity operator through $l^k_{\infty}$ on the quasi-normed spaces.

• Journal of Electrical Engineering and Technology
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• v.12 no.1
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• pp.72-77
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• 2017

This paper proposes the explicit tuning rule of multi-loop PID controller for brushless direct current motors to predict the system behaviors in time and frequency domains, using properties of the convex combination method. The convex set of the proposed controllers formulates the envelope to satisfy the performances in time and frequency domains. The final control parameters are determined by solving the convex optimization problem subject to the constraints which are represented as convex set of time domain performances. The effectiveness of the proposed control method is shown in the numerical simulation, in which controller tuning algorithm and dynamics of brushless DC motor are well taken into account.

• Journal of the Korean Operations Research and Management Science Society
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• v.22 no.3
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• pp.11-22
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• 1997

The aim of this paper is to develop the B & B type algorithms for globally minimizing concave function under 0-1 knapsack constraint. The linear convex envelope underestimating the concave object function is introduced for the bounding operations which locate the vertices of the solution set. And the simplex containing the solution set is sequentially partitioned into the subsimplices over which the convex envelopes are calculated in the candidate problems. The adoption of cutting plane method enhances the efficiency of the algorithm. These mean valid inequalities with respect to the integer solution which eliminate the nonintegral points before the bounding operation. The implementations are effectively concretized in connection with the branching stategys.

• Journal of the Korea Convergence Society
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• v.7 no.5
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• pp.213-219
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• 2016

This paper presents a branch-and-bound algorithm for solving the concave minimization problem with upper bounded variables whose single constraint is linear. The algorithm uses simplex as partition element. Because the convex envelope which most tightly underestimates the concave function on the simplex is uniquely determined by solving the related linear equations. Every branching process generates two subsimplices one lower dimensional than the candidate simplex by adding 0 and upper bound constraints. Subsequently the feasible points are partitioned into two sets. During the bounding process, the linear programming problems defined over subsimplices are minimized to calculate the lower bound and to update the incumbent. Consequently the simplices which do certainly not contain the global minimum are excluded from consideration. The major advantage of the algorithm is that the subproblems are defined on the one less dimensinal space. It means that the amount of work required for the subproblem decreases whenever the branching occurs. Our approach can be applied to solving the concave minimization problems under knapsack type constraints.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2003.11a
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• pp.60-65
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• 2003

In this study, for estimating responses of a controlled structure and determining the maximum control force of velocity-dependent damping devices, three estimation models such as Fourier envelope convex model, probability model, and Newmark design spectrum are used. For this purpose, a procedure proposed by Gupta (1990) for estimating spectral velocity using pseudo-spectral velocity which is given by the estimation models is used and modified to consider the effects of increased damping ratio by the damping device. Time history results indicate that Newmark design spectrum gives the best estimation of maximum control force for over all period structures.

• Wind and Structures
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• v.29 no.5
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• pp.323-337
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• 2019

Wind tunnel testing technique has been established as a powerful experimental method for predicting wind-induced loads on high-rise buildings. Accurate assessment of the design wind load combinations for tall buildings on the basis of wind tunnel tests is an extremely important and complicated issue. The traditional design practice for determining wind load combinations relies partly on subjective judgments and lacks a systematic and reliable method of evaluating critical load cases. This paper presents a novel optimization-based framework for determining wind tunnel derived load cases for the structural design of wind sensitive tall buildings. The peak factor is used to predict the expected maximum resultant responses from the correlated three-dimensional wind loads measured at each wind angle. An optimized convex hull is further developed to serve as the design envelope in which the peak values of the resultant responses at any azimuth angle are enclosed to represent the critical wind load cases. Furthermore, the appropriate number of load cases used for design purposes can be predicted based on a set of Pareto solutions. One 30-story building example is used to illustrate the effectiveness and practical application of the proposed optimization-based technique for the evaluation of peak resultant wind-induced load cases.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.14 no.6
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• pp.503-511
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• 2004

In this study, for estimating responses of a controlled structure and determining the maximum control force of velocity-dependent damping devices, three estimation models such as Fourier envelope convex model, probability model, and Newmark design spectrum are used. For this purpose, a procedure is proposed for estimating actual velocity using pseudo-velocity and this procedure considers the effects of damping ratio increased by the damping device. Time history results indicate that actual velocity should be used for estimating accurate maximum control force of damping device and Newmark design spectrum modified by the proposed equation gives the best estimation results for over all period structures.