• East Asian mathematical journal
• /
• 제33권1호
• /
• pp.83-102
• /
• 2017

The main purpose of this paper is to introduce a pair new class of primal and dual problem associated with an operator. We prove the sufficient optimality theorem, weak duality theorem and strong duality theorem for these problems. The equivalence between the generalized optimization problems and the generalized variational inequality problems is studied in ordered topological vector space modeled in Hilbert spaces. We introduce the concept of partial differential associated (PDA)-operator, PDA-vector function and PDA-antisymmetric function to show the existence of a new class of function called, ($T_{\eta};{\xi}_{\theta}$)-invex functions. We discuss first and second kind of ($T_{\eta};{\xi}_{\theta}$)-invex functions and establish their existence theorems in ordered topological vector spaces.

• East Asian mathematical journal
• /
• 제26권1호
• /
• pp.25-38
• /
• 2010

In this paper, we introduce a hybrid iterative method for finding a common element of the set of solutions of a mixed equilibrium problem, the set of common mixed points of finitely many nonexpansive mappings and the set of solutions of the variational inequality for an inverse strongly monotone mapping in a Hilbert space. We show that the iterative sequences converge strongly to a common element of the three sets. The results extended and improved the corresponding results of L.-C.Ceng and J.-C.Yao.

• 한국정밀공학회지
• /
• 제16권3호통권96호
• /
• pp.208-214
• /
• 1999

The purpose of this paper is to develop a profile modification technique of spur gears and its computer program for the prevention of gear tooth overlap. In the gear system, tooth overlap produces an impact at the initial contact of some tooth pairs. In this analysis, contact surface was assumed to be unbonded and frictionless under small deformation and stain. The problem is formulated by a variational statement with inequality constraint. Tooth load sharing is obtained by the application of contact theory, and overlap is known by the analysis of deformation. After carrying out the profile modification of gear tooth, we verified the reasonable results.

• 대한교통학회지
• /
• 제21권6호
• /
• pp.77-88
• /
• 2003

동적통행배정모형을 이용해서 교통정보를 ㅈ공하기 위해서는 다양한 여행자의 경로선택행태를 고려하는 것이 필요하다. 여행자계층은 일반적으로 3가지 형태로 분류된다: 1) 버스나 지하철과 같은 대중교통의 고정된 경로(fixed route class)를 이용하는 그룹, 2) 자신이 인지하는 경로비용을(perceived route, unguided class) 판단하여 경로를 선택하는 그룹, 3) 정확한 경로선택에 대한 정보를(guided class)기반으로 경로를 선택하는 그룹. 본 연구에서는 이 3그룹의 여행자를 포함하는 동적통행배정모형의 해법을 제안한다. 제안된 해법에서는 링크의 교통량과 유출교통류를 진입교통류 단일변수로 축소하여 시간과 공간을 확장하기 않고 실재의 네트워크에서 최단경로를 도출하는 방법을 적용한다. 따라서 시간종속적인 통행비용함수에 진입교통유율, 교통량, 유출교통유율 3가지 변수를 고려해야 하는 시공간확장방법에 비해 네트워크의 규모와 수행시간에 있어 유리하다.

• KSII Transactions on Internet and Information Systems (TIIS)
• /
• 제13권3호
• /
• pp.1164-1183
• /
• 2019

The rapid development of cloud computing and high requirements of operators requires strong support from the underlying Data Center Networks. Therefore, the effectiveness of using resources in the data center networks becomes a point of concern for operators and material for research. In this paper, we discuss the online virtual-cluster provision problem for multiple tenants with an aim to decide when and where the virtual cluster should be placed in a data center network. Our objective is maximizing the total revenue for the data center networks under the constraints. In order to solve this problem, this paper divides it into two parts: online multi-tenancy scheduling and virtual cluster placement. The first part aims to determine the scheduling orders for the multiple tenants, and the second part aims to determine the locations of virtual machines. We first approach the problem by using the variational inequality model and discuss the existence of the optimal solution. After that, we prove that provisioning virtual clusters for a multi-tenant data center network that maximizes revenue is NP-hard. Due to the complexity of this problem, an efficient heuristic algorithm OMS (Online Multi-tenancy Scheduling) is proposed to solve the online multi-tenancy scheduling problem. We further explore the virtual cluster placement problem based on the OMS and propose a novel algorithm during the virtual machine placement. We evaluate our algorithms through a series of simulations, and the simulations results demonstrate that OMS can significantly increase the efficiency and total revenue for the data centers.