• Management Science and Financial Engineering
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• v.18 no.2
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• pp.19-22
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• 2012

In the bin-packing problem, we deal with how to pack the items by using a minimum number of bins. In the inverse bin-packing number problem, IBPN for short, we are given a list of items and a fixed number of bins. The objective is to perturb at the minimum cost the item-size vector so that all items can be packed into the prescribed number of bins. We show that IBPN is NP-hard and provide an approximation algorithm. We also consider a variant of IBPN where the prescribed solution value should be returned by a pre-selected specific approximation algorithm.

• Communications of the Korean Mathematical Society
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• v.27 no.2
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• pp.243-255
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• 2012

In this paper, we deal with an inverse problem for electrical resistor networks to detect the location of nodes where an extraordinary currents ow into or out of the nodes proportional to the potentials on them. To achieve the goal, we solve a special type of mixed boundary value problem for Laplace equations with potential terms on rectangular networks which plays a role as a forward problem. Then we solve an inverse problem to develop an algorithm to locate the node where the extraordinary current flows on it at most four times of measurements of potential and current on its boundary.

• International Journal of Aeronautical and Space Sciences
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• v.3 no.2
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• pp.46-58
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• 2002

An inverse method is introduced to construct benchmark problems for the numerical solution of initial value problems. Benchmark problems constructed through this method have a known exact solution, even though analytical solutions are generally not obtainable. The solution is constructed such that it lies near a given approximate numerical solution, and therefore the special case solution can be generated in a versatile and physically meaningful fashion and can serve as a benchmark problem to validate approximate solution methods. A smooth interpolation of the approximate solution is forced to exactly satisfy the differential equation by analytically deriving a small forcing function to absorb all of the errors in the interpolated approximate solution. A multi-variable orthogonal function expansion method and computer symbol manipulation are successfully used for this process. Using this special case exact solution, it is possible to directly investigate the relationship between global errors of a candidate numerical solution process and the associated tuning parameters for a given code and a given problem. Under the assumption that the original differential equation is well-posed with respect to the small perturbations, we thereby obtain valuable information about the optimal choice of the tuning parameters and the achievable accuracy of the numerical solution. Illustrative examples show the utility of this method not only for the ordinary differential equations (ODEs) but for the partial differential equations (PDEs).

• 제어로봇시스템학회:학술대회논문집
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• 1996.10a
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• pp.324-327
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• 1996

This paper describes the robust controller design methods applied to the problem of an automatic system for tow-vehicle/trailer combinations. This study followed an inverse Linear Quadratic Regulator(LQR) approach which combines pole assignment methods with conventional LOR methods. It overcomes two concerns associated with these separate methods. It overcomes the robustness problems associated with pole placement methods and trial and error required in the application of the LQR problem. Moreover, a Kalman filter is used as the observer, but is modified by using the loop transfer recovery (LTR) technique with modified transmission zero assignment. The proposed inverse LQG,/LTR controllers enhances the forward motion stability and maneuverability of the combination vehicles. At high speeds, where the inherent yaw damping of the vehicle system decreases, the controller operates to maintain an adequate level of yaw damping. At backward moton, both 4WS (2WS tow-vehicle, 2WS trailer) and 6WS (4WS tow-vehicle, 2WS trailer) control laws are proposed by using inverse LQG/LTR method. To evaluate the stability and robustness of the proposed controllers, simulations for both forward and backward motion were conducted using a detailed nonlinear model. The proposed controllers are significantly more robust than the previous controllers and continues to operate effectively in spite of parameter perturbations that would cause previous controllers to enters limit cycles or to loose stability.

• The Journal of Korea Robotics Society
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• v.7 no.1
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• pp.35-44
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• 2012

This paper presents a method to optimize motion planning for industrial manipulators with redundancy. For optimal motion planning, first of all, particular inverse kinematic solution is needed to improve efficiency for manipulators with redundancy working in various environments. In this paper, we propose three kinds of methods for solving inverse kinematics problems; numerical and combined approach. Also, we introduce methods for optimal motion planning using potential function considering the order of priority. For efficient movement in industrial settings, this paper presents methods to plan motions by considering colliding obstacles, joint limits, and interference between whole arms. To confirm improved performance of robot applying the proposed algorithms, we use two kinds of robots with redundancy. One is a single arm robot with 7DOF and another is a dual arm robot with 15DOF which consists of left arm, right arm with each 7DOF, and a torso part with 1DOF. The proposed algorithms are verified through several numerical examples as well as by real implementation in robot controllers.

• Journal of The Korean Society of Agricultural Engineers
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• v.55 no.4
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• pp.1-11
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• 2013

Unsaturated hydraulic conductivity function is one of key parameters to solve the flow phenomena in problems of landslide. Prediction models for hydraulic conductivity function related to soil-water retention curve equations in many geotechnical applications have been still used instead of direct measurement of the hydraulic conductivity function since prediction models from soil-water retention curve equations are attractive for their fast and easy use and low cost. However, many researchers found that prediction models for the hydraulic conductivity function can not predict the hydraulic conductivity exactly in comparison with experimental outputs. This research introduced an inverse analysis to evaluate the hydraulic conductivity function corresponding to experimental output from the flow pump system. Optimisation process was carried out to obtain the hydraulic conductivity function. This research showed that the inverse analysis with flow pump system was suitable to assess the hydraulic conductivity in unsaturated soil, and the prediction models for the hydraulic conductivity were led to the significant discrepancy from actual experimental outputs.

• Journal of the Korean Institute of Telematics and Electronics B
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• v.29B no.9
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• pp.37-49
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• 1992

The standard definition of computational vision is a set of inverse problems of recovering surfaces from images. Thus the common characteristics of the most early vision problems are ill-posed. The main idea for solving ill-posed problems is to restrict the class of admissible solutions by introducing suitable a priori knowledge. Standard regurarization methods lead to satisfactory solutions of early vision problems but cannot deal effectively and directly with a few general problems, such as discontinuity and fusion of information from multiple modules. In this paper, we discuss limitations of standard regularization theory and present new stochastic method. We will outline a rigorous approach to overcome part of ill-posedness of image restoration, edge detection, and stereo vision problems, based on Bayes estimation and MRF(Markov random field) model, that effectively deals with the problems. This result makes one hope that this framework could be useful in the solution of other vision problems.

• Korean Journal of Mathematics
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• v.25 no.4
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• pp.469-481
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• 2017

In this paper, we established a general nonconvex split variational inequality problem, this is, an extension of general convex split variational inequality problems in two different Hilbert spaces. By using the concepts of prox-regularity, we proved the convergence of the iterative schemes for the general nonconvex split variational inequality problems. Further, we also discussed the iterative method for the general convex split variational inequality problems.

• Journal of the Korean Mathematical Society
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• v.52 no.2
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• pp.373-388
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• 2015

In this paper, a novel parallel hybrid iterative method is proposed for finding a common element of the set of solutions of a system of equilibrium problems, the set of solutions of variational inequalities for inverse strongly monotone mappings and the set of fixed points of a finite family of nonexpansive mappings in Hilbert space. Strong convergence theorem is proved for the sequence generated by the scheme. Finally, a parallel iterative algorithm for two finite families of variational inequalities and nonexpansive mappings is established.

• Bulletin of the Korean Mathematical Society
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• v.52 no.5
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• pp.1669-1681
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• 2015

In this paper, we provide semi-convergence results of the parameterized inexact Uzawa method with singular preconditioners for solving singular saddle point problems. We also provide numerical experiments to examine the effectiveness of the parameterized inexact Uzawa method with singular preconditioners.