• Proceedings of the Korean Institute of Information and Commucation Sciences Conference
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• 2004.05a
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• pp.77-79
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• 2004

Optimization of the biphenile chloromethylation process with paraphormaldegide has been done in the presence of ZnCl$_2$ with HCI gas by the Box-Wilson method of mathematical planning of experiment. The 4, 4'-( dichloromethyl)-biphenile yield dependence on the biphenile - paraphormaldegide ratio, temperature and reaction duration has been studied. A mathematical model of the process has been developed and optimal conditions for the biphenile chloromethylation procedure has been determined

• Communications of the Korean Mathematical Society
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• v.16 no.4
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• pp.667-677
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• 2001

We consider a nonsmooth multiobjective opimization problem(PE) involving locally Lipschitz functions and define gen-eralized invexity for locally Lipschitz functions. Using Fritz John type optimality conditions, we establish Fritz John type sufficient optimality theorems for (PE) under generalized invexity.

• Communications of the Korean Mathematical Society
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• v.31 no.4
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• pp.879-893
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• 2016

In this paper, we introduce three subgradient extragradient algorithms for solving pseudomonotone equilibrium problems. The paper originates from the subgradient extragradient algorithm for variational inequalities and the extragradient method for pseudomonotone equilibrium problems in which we have to solve two optimization programs onto feasible set. The main idea of the proposed algorithms is that at every iterative step, we have replaced the second optimization program by that one on a specific half-space which can be performed more easily. The weakly and strongly convergent theorems are established under widely used assumptions for bifunctions.

• Journal of the Speleological Society of Korea
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• no.73
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• pp.1-8
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• 2006

Optimization of the biphenile chloromethylation process with paraphormaldegide has been done in the presence of $ZnCl_2$ with HCl gas by the Box-Wilson method of mathematical planning of experiment. The 4,4'-(dichloromethyl)-biphenile yield dependence on the piphenile -paraphormaldegide ratio, temperature and reaction duration has been studied. A mathematical model of the process has been developed and optimal conditions for the biphenile chloromethylation procedure has been determined.

• Journal of the Chungcheong Mathematical Society
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• v.37 no.1
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• pp.41-55
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• 2024

The nonconvex and nonsmooth optimization problem has been widely applicable in image processing and machine learning. In this paper, we propose an extension of the proximal iteratively reweighted ℓ₁ algorithm for nonconvex and nonsmooth minmization problem. We assume the co-coerciveness of a term of objective function instead of Lipschitz gradient condition, which is generalized property of Lipschitz continuity. We prove the global convergence of the proposed algorithm. Numerical results show that the proposed algorithm converges faster than original proximal iteratively reweighed algorithm and existing algorithms.

• Proceedings of the Korea Society for Simulation Conference
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• 1994.10a
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• pp.1-2
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• 1994

With the prevalence of computers in modern organizations, simulation is receiving more atention as an effectvie decision -making tool. Simualtion is a computer-based numerical technique which uses mathmatical and logical models to approximate the behaviror of a real-world system. However, iptimization of synamic stochastic systems often defy analytical and algorithmic soluions. Although a simulation approach is often free fo the liminting assumption s of mathematical modeling, cost and time consiceration s make simulation the henayst's last resort. Therefore, whenever possible, analytical and algorithmica solutions are favored over simulation. This paper discussed the issues and procedrues for using simulation as a tool for optimization of stochastic complex systems that are dmodeled by computer simulation . Its emphasis is mostly on issues that are speicific to simulation optimization instead of consentrating on the general optimizationand mathematical programming techniques . A simulation optimization problem is an optimization problem where the objective function. constraints, or both are response that can only be evauated by computer simulation. As such, these functions are only implicit functions of decision parameters of the system, and often stochastic in nature as well. Most of optimization techniqes can be classified as single or multiple-resoneses techniques . The optimization of single response functins has been researched extensively and consists of many techniques. In the single response category, these strategies are gradient based search techniques, stochastic approximate techniques, response surface techniques, and heuristic search techniques. In the multiple response categroy, there are basically five distinct strategies for treating the responses and finding the optimum solution. These strategies are graphica techniqes, direct search techniques, constrained optimization techniques, unconstrained optimization techniques, and goal programming techniques. The choice of theprocedreu to employ in simulation optimization depends on the analyst and the problem to be solved. For many practival and industrial optimization problems where some or all of the system components are stochastic, the objective functions cannot be represented analytically. Therefore, modeling by computersimulation is one of the most effective means of studying such complex systems. In this paper, after discussion of simulation optmization techniques, the applications of above techniques will be presented in the modeling process of many flexible manufacturing systems.

• Communications of the Korean Mathematical Society
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• v.4 no.1
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• pp.5-15
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• 1989

• ETRI Journal
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• v.46 no.3
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• pp.367-378
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• 2024

We propose a number-theory-based quantized mathematical optimization scheme for various NP-hard and similar problems. Conventional global optimization schemes, such as simulated and quantum annealing, assume stochastic properties that require multiple attempts. Although our quantization-based optimization proposal also depends on stochastic features (i.e., the white-noise hypothesis), it provides a more reliable optimization performance. Our numerical analysis equates quantization-based optimization to quantum annealing, and its quantization property effectively provides global optimization by decreasing the measure of the level sets associated with the objective function. Consequently, the proposed combinatorial optimization method allows the removal of the acceptance probability used in conventional heuristic algorithms to provide a more effective optimization. Numerical experiments show that the proposed algorithm determines the global optimum in less operational time than conventional schemes.

• Journal of the Korean Institute of Intelligent Systems
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• v.25 no.2
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• pp.105-110
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• 2015

This study proposes the more improved mathematical model than conventional that for the 3-DOF Helicopter System in Quanser Inc., and checks the validity about the proposed model by performance comparison between the controller based on the conventional model and that based on the proposed model. Research process is next : First, analyze the dynamics for the 3-DOF helicopter system and establish the linear mathematical model. Second, check the eliminated nonlinear-elements in linearization process for establishing the linear mathematical model. And establish the improved mathematical model including the parameters corresponding to the eliminated nonlinear-elements. At that time, it is used for modeling that Particle Swarm Optimization algorithm the meta-heuristic global optimization method. Finally, design the controller based on the proposed model, and verify the validity of the proposed model by comparison about the experimental results between the designed controller and the controller based on the conventional model.

• Journal of the Korean Society of Marine Environment & Safety
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• v.23 no.7
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• pp.933-940
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• 2017

Draught and trim conditions are highly related to the loading condition of a vessel and are important factors in predicting ship manoeuverability. This paper estimates hydrodynamic coefficients from sea trial measurements with three different trim and draught conditions. A mathematical optimization method for system identification was applied to estimate the forces and moment acting on the hull. Also, fast time simulation software based on the Rheinmetall Defense model was applied to the whole estimation process, and a 4,500 Twenty-foot Equivalent Unit (TEU) class container carrier was chosen to collect sets of measurement data. Simulation results using both optimized coefficients and newly-calculated coefficients for validation agreed well with benchmark data. The results show mathematical optimization using sea measurement data enables hydrodynamic coefficients to be estimated more simply.