• 충청수학회지
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• 제29권1호
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• pp.29-35
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• 2016

In this paper, we consider a convex optimization problem with a convex integrable objective function and a geometric constraint set. We characterize the solution set of the problem when we know its one solution.

• 한국국방경영분석학회지
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• 제29권2호
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• pp.61-80
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• 2003

A fire sequencing problem is considered. Fire sequencing problem is a kind of scheduling problem that seeks to minimize the overall time span under a result of weapon­target allocation problem. The assigned weapons should impact a target simultaneously and a weapon cannot transfer the firing against another target before all planned rounds are consumed. The computational complexity of the fire sequencing problem is strongly NP­complete even if the number of weapons is two, so it is difficult to get the optimal solution in a reasonable time by the mathematical programming approach. Therefore, a genetic algorithm is adopted as a solution method, in which the representation of the solution, crossover and mutation strategies are applied on a specific condition. Computational results using randomly generated data are presented. We compared the solutions given by CPLEX and the genetic algorithm. Above $7(weapon){\times}15(target)$ size problems, CPLEX could not solve the problem even if we take enough time to solve the problem since the required memory size increases dramatically as the number of nodes expands. On the other hand, genetic algorithm approach solves all experimental problems very quickly and gives good solution quality.

• Journal of applied mathematics & informatics
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• 제9권2호
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• pp.717-730
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• 2002

In this paper we use measure theory to solve a wide range of the nonlinear programming problems. First, we transform a nonlinear programming problem to a classical optimal control problem with no restriction on states and controls. The new problem is modified into one consisting of the minimization of a special linear functional over a set of Radon measures; then we obtain an optimal measure corresponding to functional problem which is then approximated by a finite combination of atomic measures and the problem converted approximately to a finite-dimensional linear programming. Then by the solution of the linear programming problem we obtain the approximate optimal control and then, by the solution of the latter problem we obtain an approximate solution for the original problem. Furthermore, we obtain the path from the initial point to the admissible solution.

• Nonlinear Functional Analysis and Applications
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• 제26권1호
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• pp.65-70
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• 2021

We characterize the solution set for a second-order cone linear fractional optimization problem (P). We present sequential Lagrange multiplier characterizations of the solution set for the problem (P) in terms of sequential Lagrange multipliers of a known solution of (P).

• 한국항공운항학회지
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• 제16권2호
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• pp.21-27
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• 2008

An inverse method is introduced to construct the problem for the error analysis of the numerical solution of initial value problem. These problems constructed through this method have a known exact solution, even though analytical solutions are generally not obtainable. The process leading to the exact solution makes use of an initially available approximate numerical solution. 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. Using this special case exact solution, it is possible to investigate the relationship between global errors of a candidate numerical solution process and the associated tuning parameters for 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.

• 경영과학
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• 제12권2호
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• pp.63-75
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• 1995

The uncapacitated facility location problem considered here is to determine facility location sites, minimizing the total cost of establishing facilities and serving customer demand points which require primary and back-up services. To solve this problem effectively, we propose two things in this study. First, we propose an idea of Benders' decomposition approach as a solution method of the problem. Second, we implement the problem on GAMS. Using GAMS (general Algebraic Modeling System) can utilize an mixed-integer programming solver such as ZOOM/XMP and provide a completely general automated implementation with a proposed solution method.

• Journal of applied mathematics & informatics
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• 제18권1_2호
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• pp.273-286
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• 2005

Parameter identification problem of a three species (predator, mutualist-prey, and mutualist) ecological system with reaction-diffusion phenomenon is investigated in this paper. The mathematical model of the parameter identification problem is constructed and continuous dependence of the solution for the direct problem on the parameters identified is obtained. Finally, the existence of optimal solution and an optimality necessary condition for the parameter identification problem are given.

• Journal of applied mathematics & informatics
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• 제16권1_2호
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• pp.279-287
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• 2004

In this paper, we establish relations between a solution of a vector continuous-time program and a solution of a vector variational-type inequality problem with functionals.

• Coupled systems mechanics
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• 제9권1호
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• pp.77-89
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• 2020

This study is dedicated to the dynamic elasticity problem for a semi-strip. The semi-strip is loaded by the dynamic load at the center of its short edge. The conditions of fixing are given on the lateral sides of the semi-strip. The initial problem is reduced to one-dimensional problem with the help of Laplace's and Fourier's integral transforms. The one-dimensional boundary problem is formulated as the vector boundary problem in the transform's domain. Its solution is constructed as the superposition of the general solution for the homogeneous vector equation and the partial solution for the inhomogeneous vector equation. The matrix differential calculation is used for the deriving of the general solution. The partial solution is constructed with the help of Green's matrix-function, which is searched as the bilinear expansion. The case of steady-state oscillations is considered. The problem is reduced to the solving of the singular integral equation. The orthogonalization method is applied for the calculations. The stress state of the semi-strip is investigated for the different values of the frequency.

• 대한수학회논문집
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• 제10권3호
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• pp.751-758
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• 1995

We prove the existence of solution for a Dirichlet singular boundary value problem. The proofs are based on the method of upper and lower solutions.