• 대한수학회지
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• 제50권1호
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• pp.95-109
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• 2013

The aim of this paper is to establish variational principle on cone metric spaces and to give some existence theorems of solutions for equilibrium problems on cone metric spaces. We give some equivalences of an existence theorem of solutions for equilibrium problems on cone metric spaces.

• 대한수학회보
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• 제48권6호
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• pp.1225-1233
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• 2011

In this paper, without assumption of monotonicity, we study the compactness and the connectedness of the weakly efficient solutions set to vector equilibrium problems by using scalarization method in locally convex spaces. Our results improve the corresponding results in [X. H. Gong, Connectedness of the solution sets and scalarization for vector equilibrium problems, J. Optim. Theory Appl. 133 (2007), 151-161].

• 대한수학회논문집
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• 제31권4호
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• pp.879-893
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• 2016

In this paper, we introduce three subgradient extragradient algorithms for solving pseudomonotone equilibrium problems. The paper originates from the subgradient extragradient algorithm for variational inequalities and the extragradient method for pseudomonotone equilibrium problems in which we have to solve two optimization programs onto feasible set. The main idea of the proposed algorithms is that at every iterative step, we have replaced the second optimization program by that one on a specific half-space which can be performed more easily. The weakly and strongly convergent theorems are established under widely used assumptions for bifunctions.

• Nonlinear Functional Analysis and Applications
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• 제27권1호
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• pp.83-97
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• 2022

In this paper, we introduce and study generalized mixed operator quasi-equilibrium problems(GMQOEP) in Hausdorff topological vector spaces and prove the existence results for the solution of (GMQOEP) in compact and noncompact settings by employing 1-person game theorems. Moreover, using coercive condition, hemicontinuity of the functions and KKM theorem, we prove new results on the existence of solution for the particular case of (GMQOEP), that is, generalized mixed operator equilibrium problem (GMOEP).

• East Asian mathematical journal
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• 제25권4호
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• pp.505-516
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• 2009

In this paper, we consider a new class of generalized mixed vector equilibrium-like problems in Banach spaces. By using Fan-KKM Theorem and Nadler's Theorem, we prove the existence theorem of solution for this class of generalized mixed vector equilibrium-like problems.

• Journal of Information Processing Systems
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• 제13권2호
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• pp.417-427
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• 2017

Power allocation is an important factor for cognitive radio networks to achieve higher communication capacity and faster equilibrium. This paper considers power allocation problem to each cognitive user to maximize capacity of the cognitive systems subject to the constraints on the total power of each cognitive user and the interference levels of the primary user. Since this power control problem can be formulated as a mixed-integer nonlinear programming (NP) equivalent to variational inequality (VI) problem in convex polyhedron which can be transformed into complementary problem (CP), we utilize modified projection method to solve this CP problem instead of finding NP solution and give a power control allocation algorithm with a subcarrier allocation scheme. Simulation results show that the proposed algorithm performs well and effectively reduces the system power consumption with almost maximum capacity while achieve Nash equilibrium.

• 대한전기학회논문지:전력기술부문A
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• 제51권4호
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• pp.196-201
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• 2002

An important aspect of the study of power system markets involves the assessment of strategic behavior of participants for maximizing their profits. In models for imperfect competition of a deregulated system, the key tack is to find the Nash equilibrium. When the constraints are not considered in the power market, the equilibrium has the form of a pure strategy. However, the constraints are considered, the equilibrium has the form of a mired strategy. In this paper the bimatrix game approach leer finding a mixed equilibrium is analyzed. The Nash equilibrium of a mixed strategy will be used adequately for the analysis of market power.

• 호남수학학술지
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• 제35권2호
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• pp.225-234
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• 2013

Many studies of experimental economics have produced outcomes which contradict the predictions of Nash equilibrium, which relies heavily upon the premise of selfishness of an individual. In the games involving contexts of social conflicts represented by the prisoners' dilemma game, the experiments yields outcomes quite different from what are predicted by the conventional wisdom. In order to fill this gap between the conventional Nash Equilibrium and experimental outcomes, non-selfish (or other-regarding) motives of human behavior are introduced and then a new equilibrium concept, RAE-equilibrium is developed. It is also proved that an RAE-equilibrium exists under quite general conditions. Then it is applied to the prisoners' dilemma game that some of the experimental outcomes can be explained.

• Journal of applied mathematics & informatics
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• 제29권1_2호
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• pp.227-245
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• 2011

In this paper, we introduce a new iterative method for finding a common element of the set of solutions for mixed equilibrium problem, the set of solutions of the variational inequality for a ${\beta}$inverse-strongly monotone mapping and the set of fixed points of a family of finitely nonexpansive mappings in a real Hilbert space by using the viscosity and Ces$\`{a}$ro mean approximation method. We prove that the sequence converges strongly to a common element of the above three sets under some mind conditions. Our results improve and extend the corresponding results of Kumam and Katchang [A viscosity of extragradient approximation method for finding equilibrium problems, variational inequalities and fixed point problems for nonexpansive mapping, Nonlinear Analysis: Hybrid Systems, 3(2009), 475-86], Peng and Yao [Strong convergence theorems of iterative scheme based on the extragradient method for mixed equilibrium problems and fixed point problems, Mathematical and Computer Modelling, 49(2009), 1816-828], Shimizu and Takahashi [Strong convergence to common fixed points of families of nonexpansive mappings, Journal of Mathematical Analysis and Applications, 211(1) (1997), 71-83] and some authors.

• 한국정보과학회논문지:정보통신
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• 제33권2호
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• pp.183-192
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• 2006

이 논문은 QoS (Quality of Service) 네트워크 서비스를 위한 우선순위 방식의 스케줄링에서, 각 서비스 레벨의 가격을 정하는 문제를 분석한다. 특히 본 논문에서는 균형 분석 (equilibrium analysis)에 근거한 가격정책의 문제점을 파악하는 것에 중점을 둔다. 균형분석은 다음과 같은 두 가정하에 이루어진다. 첫째, 각각의 사용자들이 시스템 전체에 미치는 영향은 극히 미약하여 무시할 수 있다. 둘째, 사용자들은 전체 시스템 상태에 대한 최신의 정보를 알고 있다. 그러나 이러한 가정들은 실제 상황을 정확하게 반영하지 못하는 경우가 종종 있고, 따라서 균형분석에 의한 가격의 결정은 문제점이 있다고 본다. 본 논문에서는 시스템 작동상황을 분석하기 위해 '동적모델'을 개발하고, 이를 이용하여 현존하는 균형분석 방법의 정확성을 평가하였다. 연구결과에 의하면 균형분석은 실제적인 환경에서의 시스템의 작동 현황을 정확하게 반영하지 못하는 경우가 많은 것으로 나타났다.