• Journal of the Korea Society of Computer and Information
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• v.24 no.11
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• pp.119-126
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• 2019

The partial inverse optimization problem is an interesting variant of the inverse optimization problem in which the given instance of an optimization problem need to be modified so that a prescribed partial solution can constitute a part of an optimal solution in the modified instance. In this paper, we consider the traveling salesman problem defined on the line (TSP on the line) which has many applications such as item delivery systems, the collection of objects from storage shelves, and so on. It is worth studying the partial inverse TSP on the line, defined as follows. We are given n requests on the line, and a sequence of k requests that need to be served consecutively. Each request has a specific position on the real line and should be served by the server traveling on the line. The task is to modify as little as possible the position vector associated with n requests so that the prescribed sequence can constitute a part of the optimal solution (minimum Hamiltonian cycle) of TSP on the line. In this paper, we show that the partial inverse TSP on the line and its variant can be solved in polynomial time when the sever is equiped with a specific internal algorithm Forward Trip or with a general optimal algorithm.

• Journal of the Chungcheong Mathematical Society
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• v.29 no.1
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• pp.137-150
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• 2016

We introduce a new approach that allows us to solve, algorithmically, the contractive completion problem. In this article, we provide concrete necessary and sufficient conditions for the existence of contractive completions of Hankel partial contractions of size $4{\times}4$ using a Moore-Penrose inverse of a matrix.

• Communications of the Korean Mathematical Society
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• v.24 no.3
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• pp.467-479
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• 2009

This paper ultimately aims to develop noninvasive techniques to identify the inside of a given electrical network. Based on the theory of the partial differentiation equations and mathematical modeling, this paper devises the algorithms to find the locations of possible abnormalities. To ensure the certainty of the algorithms, this study restricted the forms of the network and the number of abnormalities, rendering it easy to prove the uniqueness of the position of the abnormalities.

• Journal of the Korean Mathematical Society
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• v.52 no.5
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• pp.1003-1021
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• 2015

A matrix completion problem has been exploited amply because of its abundant applications and the analysis of contractions enables us to have insight into structure and space of operators. In this article, we focus on a specific completion problem related to Hankel partial contractions. We provide concrete necessary and sufficient conditions for the existence of completion of Hankel partial contractions for both extremal and non-extremal types with lower dimensional matrices. Moreover, we give a negative answer for the conjecture presented in [8]. For our results, we use several tools such as the Nested Determinants Test (or Choleski's Algorithm), the Moore-Penrose inverse, the Schur product techniques, and a congruence of two positive semi-definite matrices; all these suggest an algorithmic approach to solve the contractive completion problem for general Hankel matrices of size $n{\times}n$ in both types.

• Kyungpook Mathematical Journal
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• v.57 no.2
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• pp.211-222
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• 2017

In this paper, we consider three inverse eigenvalue problems for a special type of acyclic matrices. The acyclic matrices considered in this paper are described by a graph called a broom on n + m vertices, which is obtained by joining m pendant edges to one of the terminal vertices of a path on n vertices. The problems require the reconstruction of such a matrix from given partial eigen data. The eigen data for the first problem consists of the largest eigenvalue of each of the leading principal submatrices of the required matrix, while for the second problem it consists of an eigenvalue of each of its trailing principal submatrices. The third problem has an eigenvalue and a corresponding eigenvector of the required matrix as the eigen data. The method of solution involves the use of recurrence relations among the leading/trailing principal minors of ${\lambda}I-A$, where A is the required matrix. We derive the necessary and sufficient conditions for the solutions of these problems. The constructive nature of the proofs also provides the algorithms for computing the required entries of the matrix. We also provide some numerical examples to show the applicability of our results.

• Structural Engineering and Mechanics
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• v.80 no.5
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• pp.539-551
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• 2021

With the continuous increase of computational capacity, more and more complex nonlinear elastoplastic constitutive models were developed to study the mechanical behavior of elastoplastic materials. These constitutive models generally contain a large amount of physical and phenomenological parameters, which often require a large amount of computational costs to determine. In this paper, an inverse parameter determination method is proposed to identify the constitutive parameters of elastoplastic materials, with the consideration of both strain rate effect and temperature effect. To carry out an efficient design, a hybrid optimization algorithm that combines the genetic algorithm and the Nelder-Mead simplex algorithm is proposed and developed. The proposed inverse method was employed to determine the parameters for an elasto-viscoplastic constitutive model and Johnson-cook model, which demonstrates the capability of this method in considering strain rate and temperature effect, simultaneously. This hybrid optimization algorithm shows a better accuracy and efficiency than using a single algorithm. Finally, the predictability analysis using partial experimental data is completed to further demonstrate the feasibility of the proposed method.

• Honam Mathematical Journal
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• v.37 no.3
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• pp.299-315
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• 2015

In this paper, we study the first-order system least-squares (FOSLS) spectral method for parabolic partial differential equations. There were lots of least-squares approaches to solve elliptic partial differential equations using finite element approximation. Also, some approaches using spectral methods have been studied in recent. In order to solve the parabolic partial differential equations in parallel, we consider a parallel numerical method based on a hybrid method of the frequency-domain method and first-order system least-squares method. First, we transform the parabolic problem in the space-time domain to the elliptic problems in the space-frequency domain. Second, we solve each elliptic problem in parallel for some frequencies using the first-order system least-squares method. And then we take the discrete inverse Fourier transforms in order to obtain the approximate solution in the space-time domain. We will introduce such a hybrid method and then present a numerical experiment.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.26 no.4
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• pp.213-221
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• 2013

This paper introduces a mesh continuation scheme for a one-dimensional inverse medium problem to reconstruct the spatial distribution of elastic wave velocities in heterogeneous semi-infinite solid domains. To formulate the inverse problem, perfectly-matched-layers(PMLs) are introduced as wave-absorbing boundaries that surround the finite computational domain truncated from the originally semi-infinite extent. To tackle the inverse problem in the PML-truncated domain, a partial-differential-equations(PDE)-constrained optimization approach is utilized, where a least-squares misfit between calculated and measured surface responses is minimized under the constraint of PML-endowed wave equations. The optimization problem iteratively solves for the unknown wave velocities with their updates calculated by Fletcher-Reeves conjugate gradient algorithms. The optimization is performed using a mesh continuation scheme through which the wave velocity profile is reconstructed in successively denser mesh conditions. Numerical results showed the robust performance of the mesh continuation scheme in reconstructing target wave velocity profile in a layered heterogeneous solid domain.

• Journal of the Korean Mathematical Society
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• v.53 no.5
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• pp.1133-1148
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• 2016

In this paper, we first discuss a representation of solutions to the initial value problem and the initial-boundary value problem for discrete evolution equations $${\sum\limits^l_{n=0}}c_n{\partial}^n_tu(x,t)-{\rho}(x){\Delta}_{\omega}u(x,t)=H(x,t)$$, defined on networks, i.e. on weighted graphs. Secondly, we show that the weight of each link of networks can be uniquely identified by using their Dirichlet data and Neumann data on the boundary, under a monotonicity condition on their weights.

• Journal of Korean Institute of Industrial Engineers
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• v.39 no.4
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• pp.253-259
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• 2013

Investment scenarios in the transportation network design problem usually contain installation or expansion of multi-mode transportation links. When one applies the mode choice analysis and traffic assignment sequentially for each investment scenario, it is possible that the travel impedance used in the mode choice analysis is different from the user equilibrium cost of the traffic assignment step. Therefore, to estimate the travel impedance and mode choice accurately, one needs to develop a combined model for the mode choice and traffic assignment. In this paper, we derive the inverse demand and the excess demand functions for the multi-mode multinomial logit mode choice function and develop a combined model for the multi-mode variable demand traffic assignment problem. Using data from the regional O/D and network data provided by the KTDB, we compared the performance of the partial linearization algorithm with the Frank-Wolfe algorithm applied to the excess demand model and with the sequential heuristic procedures.