• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2007.11a
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• pp.199-202
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• 2007

The similarity measure is constructed for non-convex fuzzy membership function using well known Hamming distance measure. Comparison with convex fuzzy membership function is carried out, furthermore characteristic analysis for non-convex function are also illustrated. Proposed similarity measure is proved and the usefulness is verified through example. In example, usefulness of proposed similarity is pointed out.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2008.04a
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• pp.21-22
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• 2008

Fuzzy entropy is designed for non-convex fuzzy membership function using well known Hamming distance measure. Design procedure of convex fuzzy membership function is represented through distance measure, furthermore characteristic analysis for non-convex function are also illustrated. Proof of proposed fuzzy entropy is discussed, and entropy computation is illustrated.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.9 no.1
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• pp.4-9
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• 2009

Fuzzy entropy is designed for non convex fuzzy membership function using well known Hamming distance measure. Design procedure of convex fuzzy membership function is represented through distance measure, furthermore characteristic analysis for non convex function are also illustrated. Proof of proposed fuzzy entropy is discussed, and entropy computation is illustrated.

• Nonlinear Functional Analysis and Applications
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• v.26 no.5
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• pp.1077-1089
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• 2021

In this article, we introduce the quasi strongly E-convex function and pseudo strongly E-convex function on strongly E-convex set which generalizes strongly E-convex function defined by Youness [10]. Some non trivial examples have been constructed that show the existence of these functions. Several interesting properties of these functions have been discussed. An important characterization and relationship of these functions have been established. Furthermore, a nonlinear programming problem for quasi strongly E-convex function has been discussed.

• Journal of the Korean Institute of Intelligent Systems
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• v.18 no.1
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• pp.145-149
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• 2008

The similarity measure is constructed for non-convex fuzzy membership function using well known Hamming distance measure. Comparison with convex fuzzy membership function is carried out, furthermore characteristic analysis for non-convex function are also illustrated. Proposed similarity measure is proved and the usefulness is verified through example. In example, usefulness of proposed similarity is pointed out.

• Journal of the Korea Society of Computer and Information
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• v.25 no.7
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• pp.75-83
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• 2020

We consider the D2D utility optimization problem in the cellular system. More specifically, we develop a concave function decision rule which reduces the complexity of non-convex optimization problem. Typically, utility function, which is a function of the signal and the interference, is non-convex. In this paper, we analyze the utility function from the interference perspective. We introduce the 'relative interference' and the 'interference majorization'. The relative interference captures the level of interference at D2D receiver's perspective. The interference majorization approximates the interference by applying the major interference. Accordingly, we propose a concave function decision rule, and the corresponding convex optimization solution. Simulation results show that the utility function is concave when the relative interference is less than 0.1, which is a typical D2D usage scenario. We also show that the proposed convex optimization solution can be applied for such relative interference cases.

• Korean Journal of Mathematics
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• v.27 no.4
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• pp.879-898
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• 2019

In this paper we prove some interesting inclusions concerning the numerical range of some operators and the numerical range of theirs ranges with a convex function. Further, we prove some inequalities for the numerical radius. These inclusions and inequalities are based on some classical convexity inequalities for non-negative real numbers and some operator inequalities.

• Journal of applied mathematics & informatics
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• v.16 no.1_2
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• pp.195-205
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• 2004

To the unconstrained programme of non-convex function, this article give a modified BFGS algorithm. The idea of the algorithm is to modify the approximate Hessian matrix for obtaining the descent direction and guaranteeing the efficacious of the quasi-Newton iteration pattern. We prove the global convergence properties of the algorithm associating with the general form of line search, and prove the quadratic convergence rate of the algorithm under some conditions.

• Proceedings of the KIEE Conference
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• 2004.11c
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• pp.729-731
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• 2004

This paper deals with the design of a low order $H_{\infty}$ controller by using an iterative linear matrix inequality (LMI) method. The low order $H_{\infty}$ controller is represented in terms of LMIs with a rank condition. To solve the non-convex rank-constrained LMI problem, a linear penalty function is incorporated into the objective function so that minimizing the penalized objective function subject to LMIs amounts to a convex optimization problem. With an increasing sequence of the penalty parameter, the solution of the penalized optimization problem moves towards the feasible region of the original non-convex problem. The proposed algorithm is, therefore, convergent. Numerical experiments show the effectiveness of the proposed algorithm.

• The Transactions of the Korean Institute of Electrical Engineers D
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• v.53 no.11
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• pp.747-752
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• 2004

This paper presents an iterative linear matrix inequality (LMI) approach to the design of a static output feedback (SOF) stabilization controller. A linear penalty function is incorporated into the objective function for the non-convex rank constraint so that minimizing the penalized objective function subject to LMIs amounts to a convex optimization problem. Hence, the overall procedure results in solving a series of semidefinite programs (SDPs). With an increasing sequence of the penalty parameter, the solution of the penalized optimization problem moves towards the feasible region of the original non-convex problem. The proposed algorithm is, therefore, convergent. Extensive numerical experiments are Deformed to illustrate the proposed algorithm.