• East Asian mathematical journal
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• v.25 no.1
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• pp.55-68
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• 2009

In this paper we propose new large-update primal-dual inte-rior point algorithms for $P_*(\kappa)$ linear complementarity problems(LCPs). New search directions and proximity measures are proposed based on the kernel function$\psi(t)=\frac{t^{p+1}-1}{p+1}+\frac{e^{\frac{1}{t}}-e}{e}$,$p{\in}$[0,1]. We showed that if a strictly feasible starting point is available, then the algorithm has $O((1+2\kappa)(logn)^{2}n^{\frac{1}{p+1}}log\frac{n}{\varepsilon}$ complexity bound.

• Journal of applied mathematics & informatics
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• v.3 no.2
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• pp.149-156
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• 1996

We discuss sensitivity of equilibrium points in bimatrix games depending on small variances (perturbations) of data. Applying implicit function theorem to a linear complementarity problem which is equivalent to the bimatrix game we investigate sensitivity of equi-librium points with respect to the perturbation of parameters in the game. Namely we provide the calculation of equilibrium points deriva-tives with respect to the parameters.

• Proceedings of the Korean Operations and Management Science Society Conference
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• 1992.04b
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• pp.3-9
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• 1992

참가자가 두명인 쌍행렬게임에서 각 참가자의 전략선택에 따른 이득행렬이 부정확한 상황일 경우를 고려하였다. 이러한 퍼지쌍행렬게임의 해를 구하는 방법으로 퍼지숫자간의 순위관계의 결과인 대소관계를 적용하여 선형상보문제화하는 과정을 제시하였다.

• Structural Engineering and Mechanics
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• v.12 no.1
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• pp.35-50
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• 2001

A numerical methodology is presented in this paper for the geometrically non-linear analysis of slender uni-dimensional structural elements under unilateral contact constraints. The finite element method together with an updated Lagrangian formulation is used to study the structural system. The unilateral constraints are imposed by tensionless supports or foundations. At each load step, in order to obtain the contact regions, the equilibrium equations are linearized and the contact problem is treated directly as a minimisation problem with inequality constraints, resulting in a linear complementarity problem (LCP). After the resulting LCP is solved by Lemke's pivoting algorithm, the contact regions are identified and the Newton-Raphson method is used together with path following methods to obtain the new contact forces and equilibrium configurations. The proposed methodology is illustrated by two examples and the results are compared with numerical and experimental results found in literature.

• Korean Journal of Mathematics
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• v.31 no.4
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• pp.495-504
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• 2023

This article deals with non-degenerate linear transformations on Euclidean Jordan algebras. First, we study non-degenerate for cone invariant, copositive, Lyapunov-like, and relaxation transformations. Further, we study that the non-degenerate is invariant under principal pivotal transformations and algebraic automorphisms.

• East Asian mathematical journal
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• v.26 no.1
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• pp.9-23
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• 2010

In this paper we generalize large-update primal-dual interior point methods for linear optimization problems in [2] to the $P_*(\kappa)$ linear complementarity problems based on a new kernel function which includes the kernel function in [2] as a special case. The kernel function is neither self-regular nor eligible. Furthermore, we improve the complexity result in [2] from $O(\sqrt[]{n}(\log\;n)^2\;\log\;\frac{n{\mu}o}{\epsilon})$ to $O\sqrt[]{n}(\log\;n)\log(\log\;n)\log\;\frac{m{\mu}o}{\epsilon}$.

• Proceedings of the KIEE Conference
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• 2001.07d
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• pp.2120-2122
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• 2001

This paper describes a PID controller for an attraction type magnetic levitation system considering $H^{\infty}$ performance. PID controllers are a kind of fixed structure reduced order controllers. Using change of variables a reduced order control problem can be recast into a static output feedback control problem and can be solved efficiently by LMI(Linear Matrix Inequality) method. In this paper, cone complementarity method is adopted and the simulation shows good results.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.63 no.7
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• pp.976-986
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• 2014

In this paper, the problem of reliable control of linear systems with time-varying delays, randomly occurring disturbances, and actuator failures is investigated. It is assumed that actuator failures occur when disturbances affect to the systems. Firstly, by using a suitable Lyapunov-Krasovskii functional and some recent techniques such as Wirtinger-based integral inequality and reciprocally convex approach, stabilization criterion for nominal systems with time-varying delays is derived. Secondly, the proposed method is extended to the reliable $H_{\infty}$ controller design for linear dynamic systems with time-varying delays, randomly occurring disturbances, and actuator failures. Since nonlinear matrix inequalities (NLMIs) are involved in proposed results, the cone complementarity algorithm will be introduced. Finally, two numerical examples are included to show the effectiveness of the proposed criteria.

• Kyungpook Mathematical Journal
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• v.47 no.1
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• pp.133-150
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• 2007

In a development of efficient primal-dual interior-points algorithms for self-scaled convex programming problems, one of the important properties of such cones is the existence and uniqueness of "scaling points". In this paper through the identification of scaling points with the notion of "(metric) geometric means" on symmetric cones, we extend several well-known matrix inequalities (the classical L$\ddot{o}$wner-Heinz inequality, Ando inequality, Jensen inequality, Furuta inequality) to symmetric cones. We also develop a theory of spectral geometric means on symmetric cones which has recently appeared in matrix theory and in the linear monotone complementarity problem for domains associated to symmetric cones. We derive Nesterov-Todd inequality using the spectral property of spectral geometric means on symmetric cones.

• 한국HCI학회:학술대회논문집
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• 2008.02a
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• pp.174-177
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• 2008

In 3D gaming environment, it is important to simulate the physically plausible behaviors of gaming objects in real time. In particular, rigid body dynamics consists in the heart of most game physics. In this paper, we present a constraint-based rigid body simulation method using continuous collision detection as a collision detection method, and LCP formulation as a collision response method. The continuous collision detection method never misses any collisions and thus is able to accurately report the first time of collision as well as its associated colliding features. Moreover, since the number of colliding features is typically low, it also reduces the complexity in the LCP formulation.