• Journal of the Korean Operations Research and Management Science Society
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• v.7 no.1
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• pp.11-16
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• 1982

A method is described for the solution of a linearly constrained program with parametric nonlinear objective function. The algorithm proposed in this paper may be regarded as an extension of the simplex method for parametric linear programming. Namely, it specifies the basis at each stage such that feasibility ana optimality of the original problem are satisfied by the optimal solution of the reduced parametric problem involving only nonbasic variables. It is shown that under appropriate assumptions the algorithm is finite. Parametric procedures are also indicated for solving each reduced parametric problem by maintaining the Kuhn-Tucker conditions as the parameter value varies.

• Bulletin of the Korean Mathematical Society
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• v.26 no.2
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• pp.127-134
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• 1989

This paper proposes a deformation method for solving practical nonlinear programming problems. Utilizing the nonlinear parametric programming technique with Quasi-Newton method [6,7], the method solves the problem by imbedding it into a suitable one-parameter family of problems. The approach discussed in this paper was originally developed with the aim of solving a system of structural optimization problems with frequently appears in various kind of engineering design. It is assumed that we have to solve more than one structural problem of the same type. It an optimal solution of one of these problems is available, then the optimal solutions of thel other problems can be easily obtained by using this known problem and its optimal solution as the initial problem of our parametric method. The method of nonlinear programming does not generally converge to the optimal solution from an arbitrary starting point if the initial estimate is not sufficiently close to the solution. On the other hand, the deformation method described in this paper is advantageous in that it is likely to obtain the optimal solution every if the initial point is not necessarily in a small neighborhood of the solution. the Jacobian matrix of the iteration formula has the special structural features [2, 3]. Sectioon 2 describes nonlinear parametric programming problem imbeded into a one-parameter family of problems. In Section 3 the iteration formulas for one-parameter are developed. Section 4 discusses parametric approach for Quasi-Newton method and gives algorithm for finding the optimal solution.

• Korean Journal of Computational Design and Engineering
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• v.21 no.4
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• pp.453-461
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• 2016

The trend of using Grasshopper with Rhino3D actively in architectural design process is recently spreading around the world. Well-known architects and designers such as Zaha Hadid, Patrik Schmacher is famous for using Grasshopper as their main design tool. As a tool for so-called 'Parametric Design', Grasshopper is receiving much attention all over the world. Grasshopper as a visual programming language has an advantage that designers and non-professionals of computer can easily learn it and use it to their works. However, those designers tend to make inefficient approaches with Grasshopper compared to computer programming professionals. Meanwhile, the difference between other programming languages and Grasshopper leads to the need of different approaches from other programming languages. This study aims to propose desired approaches of Grasshopper programming or scripting to be able to break through the inefficient approaches that designer is likely to make, by examining the characteristics of Grasshopper and exploring the appropriate programming approaches for Grasshopper.

• Journal of applied mathematics & informatics
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• v.24 no.1_2
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• pp.105-126
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• 2007

The purpose of this paper is to construct several parametric duality models and prove appropriate duality results under various generalized (${\theta},{\eta},{\rho}$)-V-invexity assumptions for a discrete minmax fractional programming problem involving arbitrary norms.

• Journal of applied mathematics & informatics
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• v.23 no.1_2
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• pp.1-23
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• 2007

The purpose of this paper is to develop a fairly large number of sets of global parametric sufficient optimality conditions under various generalized $({\theta},\;{\eta},\;{\rho})-V-invexity$ assumptions for a discrete minmax fractional programming problem involving arbitrary norms.

• Journal of the Korean Operations Research and Management Science Society
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• v.15 no.1
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• pp.73-82
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• 1990

This paper describes two algorithms to Nonlinear programming problems with equality constraints and with equality and inequality constraints. The first method treats nonlinear programming problems with equality constraints. Utilizing the nonlinear programming problems with equality constraints. Utilizing the nonlinear parametric programming technique, the method solves the problem by imbedding it into a suitable one-parameter family of problems. The second method is to solve a nonlinear programming problem with equality and inequality constraints, by minimizing a square sum of nonlinear functions which is derived from the Kuhn-Tucker condition.

• Journal of Institute of Control, Robotics and Systems
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• v.12 no.12
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• pp.1215-1219
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• 2006

Scheduling plays an important role in the process management in terms of providing profit-maximizing operation sequence of multiple orders and estimating completion times of them. In order to takes its full potential, varying conditions should be properly reflected in computing the schedule. The adjustment of scheduling decisions has to be made frequently in response to the occurrence of variations. It is often challenging because their model has to be adjusted and their solutions have to be computed within short time period. This paper employs Model Predictive Control(MPC) principles for updating the process condition in the scheduling model. The solutions of the resulting problems considering variations are computed using parametric programming techniques. The key advantage of the proposed framework is that repetition of solving similar programming problems with decreasing dimensionis avoided and all potential schedules are obtained before the execution of the actual processes. Therefore, the proposed framework contributes to constructing a robust decision-support tool in the face of varying environment. An example is solved to illustrate the potential of the proposed framework with remarks on potential wide applications.

• Coupled systems mechanics
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• v.7 no.6
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• pp.707-729
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• 2018

The semi-active optimal vibration control of nonlinear torsion-bar suspension vehicle systems under random road excitations is an important research subject, and the boundedness of MR dampers and the uncertainty of vehicle systems are necessary to consider. In this paper, the differential equations of motion of the coupling torsion-bar suspension vehicle system with MR damper under random road excitation are derived and then transformed into strongly nonlinear stochastic coupling vibration equations. The dynamical programming equation is derived based on the stochastic dynamical programming principle firstly for the nonlinear stochastic system. The semi-active bounded parametric optimal control law is determined by the programming equation and MR damper dynamics. Then for the uncertain nonlinear stochastic system, the minimax dynamical programming equation is derived based on the minimax stochastic dynamical programming principle. The worst-case disturbances and corresponding semi-active bounded parametric optimal control are obtained from the programming equation under the bounded disturbance constraints and MR damper dynamics. The control strategy for the nonlinear stochastic vibration of the uncertain torsion-bar suspension vehicle system is developed. The good effectiveness of the proposed control is illustrated with numerical results. The control performances for the vehicle system with different bounds of MR damper under different vehicle speeds and random road excitations are discussed.

• 제어로봇시스템학회:학술대회논문집
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• 1986.10a
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• pp.629-632
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• 1986

Both combinatorial and parametric optimization are used in computer-aided design(CAD). The most commonly occuring parametric optimization problems in engineering design such as design of control systems, design of electric circuits are usually expressed either as differentiable or as nondifferentiable semi-infinite programming(SIP) problems. In this paper we express algorithms for a class of computer-aided design problems arising in control systems.

• Journal of the Korean Institute of Intelligent Systems
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• v.20 no.6
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• pp.780-785
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• 2010

This paper introduces GP(Genetic Programming) based color detection model for an object detection and tracking. Existing color detection methods have used linear/nonlinear transformatin of RGB color-model and improved color model for illumination variation by optimization or learning techniques. However, most of cases have difficulties to classify various of colors because of interference of among color channels and are not robust for illumination variation. To solve these problems, we propose illumination robust and non-parametric multi-colors detection model using evolution of GP. The proposed method is compared to the existing color-models for various colors and images with different lighting conditions.