• KSII Transactions on Internet and Information Systems (TIIS)
• /
• v.14 no.11
• /
• pp.4595-4610
• /
• 2020

In the practical communication environment, the accurate channel state information (CSI) is difficult to obtain, which will cause the mismatch of resource and degrade the system performance. In this paper, to account for the channel uncertainties, a robust power allocation scheme for a downlink Non-orthogonal multiple access (NOMA) heterogeneous network (HetNet) is designed to maximize energy efficiency (EE), which can ensure the quality of service (QoS) of users. We conduct the robust optimization model based on worse-case method, in which the channel gains belong to certain ellipsoid sets. To solve the non-convex non-liner optimization, we transform the optimization problem via Dinkelbach method and sequential convex programming, and the power allocation of small cell users (SCUs) is achieved by Lagrange dual approach. Finally, we analysis the convergence performance of proposed scheme. The simulation results demonstrate that the proposed algorithm can improve total EE of SCUs, and has a fast convergence performance.

• Proceedings of the Korea Information Processing Society Conference
• /
• 2011.04a
• /
• pp.1240-1242
• /
• 2011

인터넷의 발달로 데이터의 양이 기하급수적으로 증가함에 따라 대용량 데이터를 효율적으로 검색하는 top k 질의 처리의 중요성이 커지고 있다. top k 는 릴레이션에서 가장 높은 (또는 가장 낮은) 스코어를 가지는 k 개의 튜플을 반환하는 방법으로, 스코어는 사용자가 정의한 스코어링 함수를 통해 계산된다. 효율적인 top k 질의 처리를 위해서는 전체 데이터 집합 중 최소한의 서브집합만 읽어서 k 개의 결과를 구할 수 있어야 한다. 이를 위해 기존 연구들은 다양한 방법의 인덱스 생성방법을 제안했다. 본 논문에서는 그 중에서 convex hull 을 사용하여 layer list 를 생성하는 기존 연구를 조사하고 문제점을 도출한다. 기존 연구 문제점 분석은 향후 연구인 스카이라인을 사용하는 top k 질의 처리 연구의 기반이 될 것으로 예상한다.

• Journal of applied mathematics & informatics
• /
• v.8 no.2
• /
• pp.473-489
• /
• 2001

The notion of difference for two convex compact sets in Rⁿ, proposed by Rubinov et al, is generalized to R/sub mxn/. A formula of the difference for the two sets, which are convex hulls of a finite number of points, is developed. In the light of this difference, the relation between Clarke generalized Jacobian and quasidifferential, in the sense of Demyanov and Rubinov, for a nonsnooth function, is established. Based on the relation, the method of estimating Clarke generalized Jacobian via quasidifferential for a certain class of function, is presented.

• Journal of the Korean Mathematical Society
• /
• v.42 no.1
• /
• pp.17-35
• /
• 2005

Necessary conditions for a deterministic optimal control problem which involves states constraints are derived in the form of a maximum principle. The conditions are similar to those of F.H. Clarke, R.B. Vinter and G. Pappas who assume that the problem's data are Lipschitz. On the other hand, our data are not continuously differentiable but only differentiable. Fermat's rule and Rockafellar's duality theory of convex analysis are the basic techniques in this paper.

• Communications of the Korean Mathematical Society
• /
• v.28 no.2
• /
• pp.419-423
• /
• 2013

In this paper we present a robust duality theory for generalized convex programming problems under data uncertainty. Recently, Jeyakumar, Li and Lee [Nonlinear Analysis 75 (2012), no. 3, 1362-1373] established a robust duality theory for generalized convex programming problems in the face of data uncertainty. Furthermore, we extend results of Jeyakumar, Li and Lee for an uncertain multiobjective robust optimization problem.

• Honam Mathematical Journal
• /
• v.20 no.1
• /
• pp.135-145
• /
• 1998

In this paper, we focus on the convex-valued selection theorem out of four main selection theorems; zero-dimensional, convex-valued, compact-valued, finite-dimensional theorems based on Michael's papers. We prove some theorems about lower semi-continuous set-valued mappings, and derive some applications to closed continuous set-valued mappings and to functional analysis. We also give a partial solution to the open problem posed by Engelking, Heath, and Michael.

• Nonlinear Functional Analysis and Applications
• /
• v.26 no.1
• /
• pp.1-11
• /
• 2021

In this paper we study the weak and strong convergence to minimizers of convex function of proximal point algorithm SP-iteration of three multivalued nonexpansive mappings in a Hilbert space.

• Nonlinear Functional Analysis and Applications
• /
• v.26 no.4
• /
• pp.781-792
• /
• 2021

In this paper, we study well-posed problems and variational inequalities in locally convex Hausdorff topological vector spaces. The necessary and sufficient conditions are obtained for the existence of solutions of variational inequality problems and quasi variational inequalities even when the underlying set K is not convex. In certain cases, solutions obtained are not unique. Moreover, counter examples are also presented for the authenticity of the main results.

• Honam Mathematical Journal
• /
• v.44 no.4
• /
• pp.513-520
• /
• 2022

The Jensen and Mercer inequalities are very important inequalities in information theory. The article provides the generalization of Mercer's inequality for convex functions on the line segments. This result contains Mercer's inequality as a particular case. Also, we investigate bounds for Shannon's entropy and give some new applications in zeta function and analysis.

• Nonlinear Functional Analysis and Applications
• /
• v.28 no.1
• /
• pp.81-93
• /
• 2023

By utilizing a certain Libera integral operator considered on analytic multivalent functions in the unit disk U. Using the hypergeometric function and the Libera integral operator, we included a new convolution operator that expands on some previously specified operators in U, which broadens the scope of certain previously specified operators. We introduced and investigated the properties of new subclasses of functions f (z) ∈ A_p using this operator.