• 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).

• Journal of applied mathematics & informatics
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• 제26권1_2호
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• pp.251-261
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• 2008

In this paper second order cone convex, second order cone pseudoconvex, second order strongly cone pseudoconvex and second order cone quasiconvex functions are introduced and their interrelations are discussed. Further a MondWeir Type second order dual is associated with the Vector Minimization Problem and the weak and strong duality theorems are established under these new generalized convexity assumptions.

• 대한수학회지
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• 제40권2호
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• pp.287-305
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• 2003

Second order necessary optimality condition for properly efficient solutions of a twice differentiable vector optimization problem is given. We obtain a nonsmooth version of the second order necessary optimality condition for properly efficient solutions of a nondifferentiable vector optimization problem. Furthermore, we prove a second order necessary optimality condition for weakly efficient solutions of a nondifferentiable vector optimization problem.

• Nonlinear Functional Analysis and Applications
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• 제26권4호
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• pp.649-662
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• 2021

Recently the author studied a one-parameter family of divergences and considered the related median minimization problem of finite points over these divergences in general symmetric cones. In this article, to utilize the results practically, we deal with a special symmetric cone called second order cone, which is important in optimization fields. To be more specific, concrete computations of divergences with its gradients and the unique minimizer of the median minimization problem of two points are provided skillfully.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제14권2호
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• pp.93-111
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• 2010

The purpose of this paper is to obtain new complexity results for a second-order cone optimization (SOCO) problem. We define a proximity function for the SOCO by a kernel function. Furthermore we formulate an algorithm for a large-update primal-dual interior-point method (IPM) for the SOCO by using the proximity function and give its complexity analysis, and then we show that the new worst-case iteration bound for the IPM is $O(q\sqrt{N}(logN)^{\frac{q+1}{q}}log{\frac{N}{\epsilon})$, where $q{\geqq}1$.

• 전기학회논문지
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• 제68권1호
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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.

• 한국항공우주학회지
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• 제49권1호
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• pp.21-30
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• 2021

탐색기를 탑재한 유도탄의 중기궤적은 탐색기 시야(FOV : Field-Of-View) 내에서 표적을 탐지하며, 전환 시점에서의 기동성을 최대화하도록 설계하는 것이 요구된다. 유도탄의 비행궤적 최적화 문제는 여러 구속조건이 적용된 비선형 문제로 일반적인 해석해를 도출하기 어렵기 때문에 그 동안 다양한 계산적인 방법들이 제시되어 왔다. 본 논문에서는 추진-활공 유도탄의 중기궤적 최적화 문제를 컨벡스 최적화 기법인 2차 원뿔 프로그래밍을 이용하여 산출하였다. 먼저, 운동방정식의 상태변수를 최소화하기 위해서 제어변수 구속조건이 추가된 제어변수 추가 형태의 운동방정식을 구성하였다. 또한, 자유 종말시간 문제와 추진시간 문제를 대처하기 위하여 정규화된 시간 변수를 독립 변수로 설정하였다. 그리고, 운동방정식과 제어변수 구속조건을 컨벡스 형태로 변환하기 위하여 각각 부분 선형화와 무손실 컨벡스 변환을 적용하였다. 마지막으로, 본 논문에서 제시된 방안의 타당성을 확인하기 위하여 비선형 최적화 프로그래밍 결과와 비교하였다.

• KSII Transactions on Internet and Information Systems (TIIS)
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• 제10권12호
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• pp.5212-5230
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• 2016

How to determine the right number of small base stations to activate in multi-cell uplinks to match traffic from a fixed quantity of K users is an open question. This paper analyses the uplink cooperative that jointly receives base stations activation to explore this question. This paper is different from existing works only consider transmitting power as optimization objective function. The global objective function is formulated as a summation of two terms: transmitting power for data and coordinated overhead for control. Then, the joint base stations activation and beamforming problem is formulated as a mixed integer second order cone optimization. To solve this problem, we develop two polynomial-time distributed methods. Method one is a two-stage solution which activates no more than K small base stations (SBSs). Method two is a heuristic algorithm by dual decomposition to MI-SOCP that activates more SBSs to obtain multiple-antennae diversity gains. Thanks to the parallel computation for each node, our methods are more computationally efficient. The strengths and weaknesses of these two proposed two algorithms are also compared using numerical results.