• Journal of applied mathematics & informatics
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• v.26 no.1_2
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• pp.375-381
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• 2008

Boundedness for the set of all the $\epsilon$-approximate solutions for convex optimization problems are considered. We give necessary and sufficient conditions for the sets of all the $\epsilon$-approximate solutions of a convex optimization problem involving finitely many convex functions and a convex semidefinite problem involving a linear matrix inequality to be bounded. Furthermore, we give examples illustrating our results for the boundedness.

• Proceedings of the Korean Society of Computer Information Conference
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• 2020.07a
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• pp.83-84
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• 2020

Sum Utility를 최적화하는 Convex Optimization Algorithm을 제안한다. 일반적으로, Sum Utility 최적화 문제는 Non Convex Optimization Problem이다. 하지만, '상대간섭'과 '간섭주요화'를 활용하여 Non Convex Optimization Problem이 간섭구간에 따라 Convex Optimization으로 해결할 수 있음을 확인하였다. 특히, 유틸리티 함수는 상대간섭 0.1 이하에서는 오목함수임을 확인하였다. 실험결과 상대간섭이 작아질수록 제안하는 알고리즘에 의한 Sum Utility는 증가함을 확인하였다.

• Journal of the Chungcheong Mathematical Society
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• v.29 no.1
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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.

• Journal of the Chungcheong Mathematical Society
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• v.27 no.3
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• pp.433-438
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• 2014

A semi-infinite optimization problem involving a quasi-convex objective function and infinitely many convex constraint functions with data uncertainty is considered. A surrogate duality theorem for the semi-infinite optimization problem is given under a closed and convex cone constraint qualification.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.27 no.8
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• pp.1353-1362
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• 2003

This paper considers a simultaneous optimization problem of structure and control systems. The problem is generally formulated as a non-convex optimization problem for the design parameters of mechanical structure and controller. Therefore, it is not easy to obtain the global solutions for practical problems. In this paper, we parameterize all design parameters of the mechanical structure such that the parameters work in the control system as decentralized static output feedback gains. Using this parameterization, we have formulated a simultaneous optimization problem in which the design specification is defined by the Η$_2$and Η$\_$$\infty$/ norms of the closed loop transfer function. So as to lead to a convex problem we approximate the nonlinear terms of design parameters to the linear terms. Then, we propose a convex optimization method that is based on linear matrix inequality (LMI). Using this method, we can surely obtain suboptimal solution for the design specification. A numerical example is given to illustrate the effectiveness of the proposed method.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.68 no.1
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• pp.159-166
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• 2019

Due to the various engagement situations, it is very difficult to generate the optimal trajectory with several constraints. This paper investigates the sequential convex programming for the impact angle control with the additional constraint of altitude limit. Recently, the SOCP(Second-Order Cone Programming), which is one area of the convex optimization, is widely used to solve variable optimal problems because it is robust to initial values, and resolves problems quickly and reliably. The trajectory optimization problem is reconstructed as convex optimization problem using appropriate linearization and discretization. Finally, simulation results are compared with analytic result and nonlinear optimization result for verification.

• Management Science and Financial Engineering
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• v.21 no.1
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• pp.11-17
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• 2015

Min-max stochastic optimization is an approach to address the distribution ambiguity of the underlying random variable. We present a unified approach to the problem which utilizes the theory of convex order on the random variables. First, we consider a general framework for the problem and give a condition under which the convex order can be utilized to transform the min-max optimization problem into a simple minimization problem. Then extremal distributions are presented for some interesting classes of distributions. Finally, applications to the single-period inventory control problems are given.

• 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.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.17 no.5
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• pp.1503-1515
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• 2023

This paper considers the jointly active and passive beamforming design in the IRS-aided MISO downlink vehicle communication system where both V2I and V2V communication paradigms coexist. We formulate the problem as an optimization problem aiming to minimize the total transmit power of the base station subject to SINR requirements of both V2I and V2V users, total transmit power of base station and IRS's phase shift constraints. To deal with this non-convex problem, we propose a method which can alternately optimize the active beamforming at the base station and the passive beamforming at the IRS. By using first-order Taylor expansion, matrix analysis theory and penalized convex-concave process method, the non-convex optimization problem with coupled variables is converted into two decoupled convex sub-problems. The simulation results show that the proposed alternate optimization algorithm can significantly decrease the total transmit power of the vehicle base station.

• Journal of applied mathematics & informatics
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• v.30 no.3_4
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• pp.413-428
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• 2012

Every contingent claim is unable to be replicated in the incomplete markets. Shortfall risk is considered with some risk exposure. We show how the dynamic optimization problem with the capital constraint can be reduced to the problem to find an optimal modified claim $\tilde{\psi}H$ where$\tilde{\psi}H$ is a randomized test in the static problem. Convex and coherent risk measures defined in the Orlicz hearts spaces, $M^{\Phi}$, are used as risk measure. It can be shown that we have the same results as in [21, 22] even though convex and coherent risk measures defined in the Orlicz hearts spaces, $M^{\Phi}$, are used. In this paper, we use Fenchel duality Theorem in the literature to deduce necessary and sufficient optimality conditions for the static optimization problem using convex duality methods.