• Journal of the Korean Mathematical Society
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• v.41 no.5
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• pp.821-864
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• 2004

Both parametric and parameter-free necessary and sufficient optimality conditions are established for a class of nondiffer-entiable nonconvex optimal control problems with generalized fractional objective functions, linear dynamics, and nonlinear inequality constraints on both the state and control variables. Based on these optimality results, ten Wolfe-type parametric and parameter-free duality models are formulated and weak, strong, and strict converse duality theorems are proved. These duality results contain, as special cases, similar results for minmax fractional optimal control problems involving square roots of positive semi definite quadratic forms, and for optimal control problems with fractional, discrete max, and conventional objective functions, which are particular cases of the main problem considered in this paper. The duality models presented here contain various extensions of a number of existing duality formulations for convex control problems, and subsume continuous-time generalizations of a great variety of similar dual problems investigated previously in the area of finite-dimensional nonlinear programming.

• International Journal of Korean Welding Society
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• v.3 no.2
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• pp.15-23
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• 2003

A genetic algorithm was applied to an arc welding process to determine near optimal settings of welding process parameters which produce good weld quality. This method searches for optimal settings of welding parameters through systematic experiments without a model between input and output variables. It has an advantage of being able to find optimal conditions with a fewer number of experiments than conventional full factorial design. A genetic algorithm was applied to optimization of weld bead geometry. In the optimization problem, the input variables were wire feed rate, welding voltage, and welding speed, root opening and the output variables were bead height, bead width, penetration and back bead width. The number of level for each input variable is 8, 16, 8 and 3, respectively. Therefore, according to the conventional full factorial design, in order to find the optimal welding conditions, 3,072 experiments must be performed. The genetic algorithm, however, found the near optimal welding conditions from less than 48 experiments.

• Journal of Welding and Joining
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• v.18 no.5
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• pp.63-69
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• 2000

A genetic algorithm was applied to an arc welding process to determine near optimal settings of welding process parameters which produce good weld quality. This method searches for optimal settings of welding parameters through systematic experiments without a model between input and output variables. It has an advantage of being able to find optimal conditions with a fewer number of experiments than conventional full factorial design. A genetic algorithm was applied to optimization of weld bead geometry. In the optimization problem, the input variables was wire feed rate, welding voltage, and welding speed and the output variables were bead height, bead width, and penetration. The number of level for each input variable is 16, 16, and 8, respectively. Therefore, according to the conventional full factorial design, in order to find the optimal welding conditions, 2048 experiments must be performed. The genetic algorithm, however, found the near optimal welding conditions from less than 40 experiments.

• Food Science and Preservation
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• v.30 no.6
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• pp.905-917
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• 2023

The optimal fermentation conditions for producing fermented black soybeans rich in sulfur-containing amino acids were investigated. Response surface methodology monitored fermentation conditions. A central composite design examined the effect of independent variables: enzyme concentration (X₁) and fermentation time (X₂) on yield and methionine content. Both factors significantly influenced these dependent variables. Enzyme concentration more profoundly affected amino nitrogen content than fermentation time. β-Glucan content and cystine level were primarily affected by fermentation time. We elicited each variable's regression formula and identified optimal fermentation conditions for functional compounds. The predicted optimum conditions were an enzyme concentration of 0.28-0.32% and a fermentation time of 58.0-62.0 min. Under these optimal conditions, each black soybean variety's sulfur amino acid content ranged from 818.62 to 922.62 mg/100 g, demonstrating significant variety differences.

• Journal of the Korean Mathematical Society
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• v.52 no.3
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• pp.567-586
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• 2015

In this paper, we study optimal control problems for parabolic hemivariational inequalities of dynamic elasticity and investigate the continuity of the solution mapping from the given initial value and control data to trajectories. We show the existence of an optimal control which minimizes the quadratic cost function and establish the necessary conditions of optimality of an optimal control for various observation cases.

• Honam Mathematical Journal
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• v.8 no.1
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• pp.21-49
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• 1986

A class of singular quadratic control problem is considered. The state is governed by a higher order system of ordinary linear differential equations and very general nonstandard boundary conditions. These conditions in many important cases reduce to standard boundary conditions and because of the conditions the usual controllability condition is not needed. In the special case where the coefficient matrix of the control variable in the cost functional is a time-independent singular matrix, the corresponding optimal control law as well as the optimal controller are computed. The method of investigation is based on the theory of least-squares solutions of multi-valued operator equations.

• Journal of applied mathematics & informatics
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• v.41 no.2
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• pp.229-245
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• 2023

In this paper, we consider cooperative elliptic systems under conjugation conditions. We first prove the existence of the state for 2 × 2 cooperative elliptic systems with Dirichlet and Neumann conditions, then we find the set of equations and inequalities that characterizes the optimal control of distributed type for these systems. The case of n × n cooperative systems is also established.

• East Asian mathematical journal
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• v.34 no.5
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• pp.683-691
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• 2018

We consider an optimal control problem for an impulsive stage-structured model involving ordinary differential equations with impulsive values of initial conditions in the next year. The main goal is to maximize a profit of the catch of Pacific cod in the South Korea through optimal harvest strategy as a control of adult cod. We established necessary conditions for the optimal harvest control using idea of Pontryagin's maximum principle. The optimal harvest strategy is to numerically solve the equation by using an iterative method with the Runge-Kutta method. Finally, we compare a monthly average of fishing mortality of Pacific cod from 2013 to 2017 with monthly fishing mortality for result obtained optimal harvest strategy.

• Journal of Microbiology and Biotechnology
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• v.18 no.6
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• pp.1115-1120
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• 2008

A novel cathepsin B inhibitor-producing bacterium was isolated from marine sediments and identified based on its 16S rDNA sequence as Pseudomonas sp. strain PB01 (Accession No. EU126129). The growth and enzyme inhibitor production were investigated under various culture conditions. A mixture of organic nitrogen source was required for the optimal production, whereas both glucose and maltose proved to be the effective carbon sources for cathepsin B inhibitor production. Other optimal culture conditions included temperature range between 25 and $28^{\circ}C$, initial medium pH of 6.6, and shaking speed of 200 rpm. Under these optimal conditions, the maximum inhibitory activity from culture broth was approximately 50% after 30 h of cultivation. Additionally, kinetic study revealed that inhibitor production paralleled with cell growth, which suggested that the inhibitor may be a primary metabolite of that bacterium.

• Journal of the Korean Society for Precision Engineering
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• v.19 no.12
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• pp.33-37
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• 2002

A short shot is a molded part that is incomplete because insufficient material was injected into the mold. Remedial actions to control the process conditions can be taken by the injection molding experts based on their knowledge and experience. However, it is very difficult for the non-experts to avoid short shot by finding the proper process conditions such as mold temperature, melt temperature and filling time. In this paper, an intelligent generator of the optimal process conditions based upon fuzzy logic algorithm is proposed so that trial and error can be minimized and the non-experts as well as the experts can also find the optimal process conditions.