• Journal of Electrical Engineering and Technology
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• v.8 no.1
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• pp.80-89
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• 2013

This paper presents an efficient approach for solving economic dispatch (ED) problems with nonconvex cost functions using a 'Mean-Variance Optimization (MVO)' algorithm with Kuhn-Tucker condition and swap process. The aim of the ED problem, one of the most important activities in power system operation and planning, is to determine the optimal combination of power outputs of all generating units so as to meet the required load demand at minimum operating cost while satisfying system equality and inequality constraints. This paper applies Kuhn-Tucker condition and swap process to a MVO algorithm to improve a global minimum searching capability. The proposed MVO is applied to three different nonconvex ED problems with valve-point effects, prohibited operating zones, transmission network losses, and multi-fuels with valve-point effects. Additionally, it is applied to the large-scale power system of Korea. The results are compared with those of the state-of-the-art methods as well.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.27 no.2
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• pp.268-275
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• 2003

Generally, structural optimization is carried out based on external static loads. All forces have dynamic characteristics in the real world. Mathematical optimization with dynamic loads is extremely difficult in a large-scale problem due to the behaviors in the time domain. The dynamic loads are often transformed into static loads by dynamic factors, design codes, and etc. Therefore, the optimization results can give inaccurate solutions. Recently, a systematic transformation has been proposed as an engineering algorithm. Equivalent static loads are made to generate the same displacement field as the one from dynamic loads at each time step of dynamic analysis. Thus, many load cases are used as the multiple leading conditions which are not costly to include in modern structural optimization. In this research, it is mathematically proved that the solution of the algorithm satisfies the Karush-Kuhn-Tucker necessary condition. At first, the solution of the new algorithm is mathematically obtained. Using the termination criteria, it is proved that the solution satisfies the Karush-Kuhn-Tucker necessary condition of the original dynamic response optimization problem. The application of the algorithm is discussed.

• Journal of applied mathematics & informatics
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• v.29 no.5_6
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• pp.1157-1165
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• 2011

The Karush-Kuhn-Tucker (KKT) necessary optimality conditions for nonlinear differentiable programming problems are also sufficient under suitable convexity assumptions. The KKT conditions in multiobjective programming problems with interval-valued objective and constraint functions are derived in this paper. The main contribution of this paper is to obtain the Pareto optimal solutions by resorting to the sufficient optimality condition.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.46 no.2
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• pp.109-115
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• 2023

This paper studied the problem of determining the optimal inventory level to meet the customer service target level in a situation where the customer demand for each branch of a nationwide retailer is uncertain. To this end, ISR (In-Stock Ratio) was defined as a key management indicator (KPI) that can be used from the perspective of a nationwide retailer such as Samsung, LG, or Apple that sells goods at branches nationwide. An optimization model was established to allow the retailer to minimize the total amount of inventory held at each branch while meeting the customer service target level defined as the average ISR. This paper proves that there is always an optimal solution in the model and expresses the optimal solution in a generalized form using the Karush-Kuhn-Tucker condition regardless of the shape of the probability distribution of customer demand. In addition, this paper studied the case where customer demand follows a specific probability distribution such as a normal distribution, and an expression representing the optimal inventory level for this case was derived.

• Bulletin of the Korean Mathematical Society
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• v.23 no.2
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• pp.141-148
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• 1986

In [1], M. Guignard considered a constraint set in a Banach space, which is similar to that in [2] and gave a first order necessary optimality condition which generalized the Kuhn-Tucker conditions [3]. Sufficiency is proved for objective functions which is either pseudoconcave [5] or quasi-concave [6] where the constraint sets are taken pseudoconvex. In this note, we consider a psedoconvex programming problem in a Hilbert space. Constraint set in a Hillbert space being pseudoconvex and the objective function is restrained by an operator equation. Then we use the methods similar to that in [1] and [6] to obtain a necessary and sufficient optimality condition.

• Proceedings of the KSR Conference
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• 2011.05a
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• pp.888-894
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• 2011

This paper is a study of optimal train driving strategy to minimize the energy consumption. Optimal driving strategy can be analyzed as an optimal problem which have constraints by using Largrangian Function and Kuhn-Tucker condition. We simulate the section between Konkuk University Station and Seongsu Station which is on outer circle line of the Seoul Metro line No.2 by using MATLAB and consider the straight level track and the speed limit.

• The Journal of the Acoustical Society of Korea
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• v.21 no.6
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• pp.522-530
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• 2002

This paper introduces a neural network (NN) -based nonlinear predictor for the LP (Linear Prediction) residual. To evaluate the effectiveness of the NN-based nonlinear predictor for LP-residual, we first compared the average prediction gain of the linear long-term predictor with that of the NN-based nonlinear long-term predictor. Then, the effects on the quantization noise of the nonlinear prediction residuals were investigated for the NN-based nonlinear predictor A new NN predictor takes into consideration not only prediction error but also quantization effects. To increase robustness against the quantization noise of the nonlinear prediction residual, a constrained back propagation learning algorithm, which satisfies a Kuhn-Tucker inequality condition is proposed. Experimental results indicate that the prediction gain of the proposed NN predictor was not seriously decreased even when the constrained optimization algorithm was employed.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.15 no.2
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• pp.281-291
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• 2002

This paper describes the minimum cost design of prestressed reinforced concrete (PRC) hem with rectangular section. The cost of construction as objective function which includes the costs of concrete, prestressing steel, non prestressing steel, and formwork is minimized. The design constraints include limits on the minimum deflection, flexural and shear strengths, in addition to ductility requirements, and upper-Lower bounds on design variables as stipulated by the specification. The optimization is carried out using the methods based on discretized continuum-type optimality criteria(DCOC). Based on Kuhn-Tucker necessary conditions, the optimality criteria are explicitly derived in terms of the design variables - effective depth, eccentricity of prestressing steel and non prestressing steel ratio. The prestressing profile is prescribed by parabolic functions. In this paper the effective depth is considered to be freely-varying and one uniform for the entire multispan beam respectively. Also the maximum eccentricity of prestressing force is considered in every span. In order to show the applicability and efficiency of the derived algorithm, several numerical examples of PRC continuous beams are solved.

• 제어로봇시스템학회:학술대회논문집
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• 2003.10a
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• pp.2246-2251
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• 2003

This paper proposes shape design of frame structures for vibration suppression and weight reduction. The $H_{\infty}$ norm of the transfer function from disturbance sources to the output points where vibration should be suppressed, is adopted as the performance index to represent the magnitude of vibration transfer. The design parameters are the node positions of the frame structure, on which constraints are imposed so that the structure achieves given tasks. For computation of Pareto optimal solutions to the two-objective design problem, a number of linear combinations of the $H_{\infty}$ norm and the total weight of the structure are considered and minimized. For minimization of the scalared objective function, a Lagrange function is defined by the objective function and the imposed constraints on the design parameters. The solution for which the Lagrange function satisfies the Karush-Kuhn-Tucker condition, is searched by the sequential quadratic programming (SQP) method. Numerical examples are presented to demonstrate the effectiveness of the proposed design method.

• 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.