• 대한수학회논문집
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• 제32권3호
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• pp.765-778
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• 2017

Finding an initial feasible solution on the central path is the main difficulty of feasible interior-point methods. Although, some algorithms have been suggested to remedy this difficulty, many practical implementations often do not use perfectly centered starting points. Therefore, it is worth to analyze the case that the starting point is not exactly on the central path. In this paper, we propose a weighted-path following interior-point algorithm for solving the Cartesian $P_{\ast}({\kappa})$-linear complementarity problems (LCPs) over symmetric cones. The convergence analysis of the algorithm is shown and it is proved that the algorithm terminates after at most $O\((1+4{\kappa}){\sqrt{r}}{\log}{\frac{x^0{\diamond}s^0}{\varepsilon}}\)$ iterations.

• Journal of applied mathematics & informatics
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• 제33권1_2호
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• pp.229-234
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• 2015

In the setting of semidefinite linear complementarity problems on $S^n$, we focus on the Stein Transformation $S_A(X):=X-AXA^T$ for $A{\in}R^{n{\times}n}$ that is positive semidefinite preserving (i.e., $S_A(S^n_+){\subseteq}S^n_+$) and show that such transformation is strictly monotone if and only if it is nondegenerate. We also show that a positive semidefinite preserving $S_A$ has the Ultra-GUS property if and only if $1{\not\in}{\sigma}(A){\sigma}(A)$.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제13권3호
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• pp.189-202
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• 2009

In this paper we propose new primal-dual interior point algorithms for $P_*(\kappa)$ linear complementarity problems based on a new class of kernel functions which contains the kernel function in [8] as a special case. We show that the iteration bounds are $O((1+2\kappa)n^{\frac{9}{14}}\;log\;\frac{n{\mu}^0}{\epsilon}$) for large-update and $O((1+2\kappa)\sqrt{n}log\frac{n{\mu}^0}{\epsilon}$) for small-update methods, respectively. This iteration complexity for large-update methods improves the iteration complexity with a factor $n^{\frac{5}{14}}$ when compared with the method based on the classical logarithmic kernel function. For small-update, the iteration complexity is the best known bound for such methods.

• Structural Engineering and Mechanics
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• 제11권2호
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• pp.171-184
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• 2001

A direct discrete formulation suitable for the nonlinear analysis of masonry structures is presented. The numerical approach requires a pair of dual meshes, one for describing displacement fields, one for imposing equilibrium. Forces and displacements are directly used (instead of having to resort to a model derived from a set of differential equations). Associated and nonassociated flow laws are dealt with within a complementarity framework. The main features of the method and of the relevant computer code are discussed. Numerical examples are presented, showing that the numerical approach is able to describe plastic strains, damage effects and crack patterns in masonry structures.

• 대한기계학회논문집
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• 제18권8호
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• pp.2026-2038
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• 1994

A numerical scheme is developed for the analysis of incipient sliding contact with orthotropic friction condition subjected to tangential load and twisting moment. The inherent nonlinearity in the orthotropic friction law has been treated by a polyhedral friction law. Then, a three-dimensional linear complementarity problem(LCP) formulation in an incremental form is obtained, and the existence of a solution is investigated. A Lemke's complementary pivoting algorithm is used for solving the LCP. The scheme is illustrated by spherical contact problems, and the effects of eccentricity of elliptical friction domain on the traction and stick region are discussed.

• 대한수학회보
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• 제46권3호
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• pp.521-534
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• 2009

In this paper we present new large-update primal-dual interior point algorithms for $P_*$ linear complementarity problems(LAPS) based on a class of kernel functions, ${\psi}(t)={\frac{t^{p+1}-1}{p+1}}+{\frac{1}{\sigma}}(e^{{\sigma}(1-t)}-1)$, p $\in$ [0, 1], ${\sigma}{\geq}1$. It is the first to use this class of kernel functions in the complexity analysis of interior point method(IPM) for $P_*$ LAPS. We showed that if a strictly feasible starting point is available, then new large-update primal-dual interior point algorithms for $P_*$ LAPS have $O((1+2+\kappa)n^{{\frac{1}{p+1}}}lognlog{\frac{n}{\varepsilon}})$ complexity bound. When p = 1, we have $O((1+2\kappa)\sqrt{n}lognlog\frac{n}{\varepsilon})$ complexity which is so far the best known complexity for large-update methods.

• Journal of applied mathematics & informatics
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• 제29권3_4호
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• pp.653-668
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• 2011

This paper presents a new hybrid method for solving nonlinear complementarity problems with $P_0$-functions. It can be regarded as a combination of smoothing trust region method with ODE-based method and line search technique. A feature of the proposed method is that at each iteration, a linear system is only solved once to obtain a trial step, thus avoiding solving a trust region subproblem. Another is that when a trial step is not accepted, the method does not resolve the linear system but generates an iterative point whose step-length is defined by a line search. Under some conditions, the method is proven to be globally and superlinearly convergent. Preliminary numerical results indicate that the proposed method is promising.

• East Asian mathematical journal
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• 제25권1호
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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 the Korean Society for Industrial and Applied Mathematics
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• 제12권4호
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• pp.227-238
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• 2008

In this paper we extend primal-dual interior point algorithm for linear optimization (LO) problems to $P_*({\kappa})$ linear complementarity problems(LCPs) ([1]). We define proximity functions and search directions based on kernel functions, ${\psi}(t)=\frac{t^{p+1}-1}{p+1}-{\log}\;t$, $p{\in}$[0, 1], which is a generalized form of the one in [16]. It is the first to use this class of kernel functions in the complexity analysis of interior point method(IPM) for $P_*({\kappa})$ LCPs. We show that if a strictly feasible starting point is available, then new large-update primal-dual interior point algorithms for $P_*({\kappa})$ LCPs have $O((1+2{\kappa})nlog{\frac{n}{\varepsilon}})$ complexity which is similar to the one in [16]. For small-update methods, we have $O((1+2{\kappa})\sqrt{n}{\log}{\frac{n}{\varepsilon}})$ which is the best known complexity so far.

• 한국조경학회지
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• 제33권4호
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• pp.45-70
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• 2005

The purpose of this study is to overview foreign trends in the study of the landscape ecology through new framework of landscape ecological studies and to suggest possibility and limitation of introduction of landscape ecology studies in Korea. Because of historical reasons rooted in different disciplines, landscape ecology of the present time is not unified at all. Therefore, landscape ecology should be understood in an integrative manner accommodating different views and various aspects of landscape(NOOS, GEOS, BIOS). Facing the increasing environmental problems and the goal of sustainable landscape, the principle of a holistic approach complementarity and transdisciplinarity outlined in this paper (esp. connection physical-materials and cognitive system) might help to understand the characteristics of landscapes and landscape ecology. Important steps towards this direction are the landscape survey, diagnosis, the identification of landscape functions, the development of landscape evaluation models and landscape planning system. Recently there have been a few landscape ecological researches in Korea, which tells there have been strong needs to solve practical landscape problems caused by the rapid socioeconomic growth for several decades. However, almost of this studies are focused on cognitive and visual aspects of landscapes defined boundaries of disciplines. But for more holistic approach complementarity and transdisciplinarity in landscape ecological studies, many other aspects such as the consideration of geoecological and bioecologocal variables, preperation of ecological basic data(mapping) and the development of landscape planning as a tool for practical application should be integrated into the whole landscape system.