• Journal of the Chungcheong Mathematical Society
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• v.33 no.1
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• pp.57-63
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• 2020

We investigate the boundedness of the spectrum of a convex base function for a new function space. The result guarantees the continuity of the Calderón-Zygmund operators on the new space.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.27 no.6
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• pp.1041-1049
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• 2003

In this paper, a new local two-point approximation method which is based on the exponential intervening variable is proposed. This new algorithm, called the Two-Point Convex Approximation(TPCA), use the function and design sensitivity information from the current and previous design points of the sequential approximate optimization to generate a sequence of convex, separable subproblems. This paper describes the derivation of the parameters associated with the approximation and the numerical solution procedure. In order to show the numerical performance of the proposed method, a sequential approximate optimizer is developed and applied to solve several typical design problems. These optimization results are compared with those of other optimizers. Numerical results obtained from the test examples demonstrate the effectiveness of the proposed method.

• Honam Mathematical Journal
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• v.40 no.3
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• pp.509-519
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• 2018

In this paper, we introduce a new class of reciprocal convex set which is called as relative reciprocal convex set. We establish a necessary and sufficient condition for the minimum of the differentiable relative reciprocal convex function. This condition can be viewed as a new class of variational inequality which is called relative reciprocal variational inequality. Using the auxiliary principle technique we discuss the existence criteria for the solution of relative reciprocal variational inequality. Some special cases which are naturally included in our main results are also discussed.

• Journal of the Korea Society for Simulation
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• v.13 no.1
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• pp.11-23
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• 2004

The decomposition of a structuring element for a morphological operation reduces the amount of the computation required for executing the operation. In this paper, we present a new technique for the decomposition of convex structuring elements for morphological operations. We formulated the linear constraints for the decomposition of a convex polygon in discrete space, then the constraints are applied to the decomposition of a convex structuring element. Also, a cost function is introduced to represent the optimal criteria for decomposition. We use linear integer programming technique to find the combination of basis structuring elements which minimizes the amount of the computation required for executing the morphological operation. Formulating different cost functions for different implementation methods and computer architectures, we can determine the optimal decompositions which guarantee the minimal amounts of computation on different computing environment.

• Kyungpook Mathematical Journal
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• v.56 no.2
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• pp.597-610
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• 2016

For a sufficiently adequate special case of the Dziok-Srivastava linear operator defined by means of the Hadamard product (or convolution) with Srivastava-Wright convolution operator, the authors investigate several mapping properties involving various subclasses of analytic and univalent functions, $G({\lambda},{\alpha})$ and $M({\lambda},{\alpha})$. Furthermore we discuss some inclusion relations for these subclasses to be in the classes of k-uniformly convex and k-starlike functions.

• Journal of the Korean Mathematical Society
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• v.44 no.4
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• pp.971-985
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• 2007

A sequential optimality condition characterizing the efficient solution without any constraint qualification for an abstract convex vector optimization problem is given in sequential forms using subdifferentials and ${\epsilon}$-subdifferentials. Another sequential condition involving only the subdifferentials, but at nearby points to the efficient solution for constraints, is also derived. Moreover, we present a proposition with a sufficient condition for an efficient solution to be properly efficient, which are a generalization of the well-known Isermann result for a linear vector optimization problem. An example is given to illustrate the significance of our main results. Also, we give an example showing that the proper efficiency may not imply certain closeness assumption.

• Proceedings of the Korean Society of Broadcast Engineers Conference
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• 2018.06a
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• pp.20-21
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• 2018

행렬의 rank 최소화 기법은 영상 잡음 제거, 행렬 완성(completion), low rank 행렬 복원 등 다양한 영상처리 분야에서 효과적으로 이용되어 왔다. 특히 nuclear norm 을 이용한 low rank 최소화 기법은 convex optimization 을 통하여 대상 행렬의 특이값(singular value)을 thresholding 함으로써 간단하게 low rank 행렬을 얻을 수 있다. 하지만, nuclear norm 을 이용한 low rank 최소화 방법은 행렬의 rank 값을 정확하게 근사하지 못하기 때문에 잡음 제거가 효과적으로 이루어지지 못한다. 본 논문에서는 영상의 잡음을 제거 하기 위해 다중 잡음 제거 영상을 이용하여 유사도가 높은 유사 패치 행렬을 구성하고, 유사 패치 행렬의 rank 를 non-convex function 을 이용하여 최소화시키는 방법을 통해 잡음을 제거하는 방법을 제안한다.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.58 no.8
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• pp.1485-1495
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• 2009

This paper presents a novel approach to economic dispatch (ED) with nonconvex fuel cost function as combinatorial optimization problems (COP) while most of the conventional researches have been developed as function optimization problems (FOP). One nonconvex fuel cost function can be divided into several convex fuel cost functions, and each convex function can be regarded as a generation type (G-type). In that case, ED with nonconvex fuel cost function can be considered as COP finding the best case among all feasible combinations of G-types. In this paper, a genetic algorithm is applied to solve the COP, and the ${\lambda}-P$ function method is used to calculate ED for the fitness function of GA. The ${\lambda}-P$ function method is reviewed briefly and the GA procedure for COP is explained in detail. This paper deals with two kinds of ED problems, namely ED with multiple fuel units (EDMF) and ED with prohibited operating zones (EDPOZ). The proposed method is tested for all the ED problems, and the test results show an improvement in solution cost compared to the results obtained from conventional algorithms.

• International Journal of Control, Automation, and Systems
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• v.6 no.4
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• pp.468-476
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• 2008

This paper presents a novel approach to economic dispatch (ED) with nonconvex fuel cost function as combinatorial optimization problems (COP) while most of the conventional researches have been developed as function optimization problems (FOP). One nonconvex fuel cost function can be divided into several convex fuel cost functions, and each convex function can be regarded as a generation type (G-type). In that case, ED with nonconvex fuel cost function can be considered as COP finding the best case among all feasible combinations of G-types. In this paper, a genetic algorithm is applied to solve the COP, and the $\lambda$-P table method is used to calculate ED for the fitness function of GA. The $\lambda$-P table method is reviewed briefly and the GA procedure for COP is explained in detail. This paper deals with three kinds of ED problems, namely ED considering valve-point effects (EDVP), ED with multiple fuel units (EDMF), and ED with prohibited operating zones (EDPOZ). The proposed method is tested for all three ED problems, and the test results show an improvement in solution cost compared to the results obtained from conventional algorithms.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.41 no.8
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• pp.917-920
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• 2016

SpSF algorithm is direction-of-arrival estimation algorithm based on sparse representation of incident signlas. Cost function to be optimized for DOA estimation is multi-dimensional nonlinear function, which is hard to handle for optimization. After some manipulation, the problem can be cast into convex optimiztion problem. Convex optimization problem tuns out to be constrained optimization problem, where the parameter in the constraint has to be determined. The solution of the convex optimization problem is dependent on the specific parameter value in the constraint. In this paper, we propose a rule-of-thumb for determining the parameter value in the constraint. Based on the fact that the noise in the array elements is complex Gaussian distributed with zero mean, the average of the Frobenius norm of the matrix in the constraint can be rigorously derived. The parameter in the constrint is set to be two times the average of the Frobenius norm of the matrix in the constraint. It is shown that the SpSF algorithm actually works with the parameter value set by the method proposed in this paper.