Book•
Linear complementarity, linear and nonlinear programming
01 Jan 1988-
About: The article was published on 1988-01-01 and is currently open access. It has received 1012 citations till now. The article focuses on the topics: Mixed complementarity problem & Complementarity theory.
Citations
More filters
Posted Content•
TL;DR: This paper presents an optimal technique to map virtual machines to physical machines (nodes) such that the number of required nodes is minimized and provides two approaches based on linear programming and quadratic programming techniques that significantly improve over the existing theoretical bounds and efficiently solve the problem of virtual machine placement in data centers.
Abstract: Cloud computing provides a computing platform for the users to meet their demands in an efficient, cost-effective way. Virtualization technologies are used in the clouds to aid the efficient usage of hardware. Virtual machines (VMs) are utilized to satisfy the user needs and are placed on physical machines (PMs) of the cloud for effective usage of hardware resources and electricity in the cloud. Optimizing the number of PMs used helps in cutting down the power consumption by a substantial amount. In this paper, we present an optimal technique to map virtual machines to physical machines (nodes) such that the number of required nodes is minimized. We provide two approaches based on linear programming and quadratic programming techniques that significantly improve over the existing theoretical bounds and efficiently solve the problem of virtual machine (VM) placement in data centers.
50 citations
Cites methods from "Linear complementarity, linear and ..."
...1 Quadratic programming The quadratic program NLP can be solved using various efficient techniques such as interior points, active set [25], gradient techniques or through the extensions of simplex algorithm [25]....
[...]
TL;DR: A generalization of the classicallinear complementarity problem is presented together with an algorithm based on the double description method for solving linear inequalities and succeeds in describing continuous as well as unbounded solution sets.
Abstract: Motivated by a number of typical applications, a generalization of the classicallinear complementarity problem is presented together with an algorithm to determine the complete solution set. The algorithm is based on the double description method for solving linear inequalities and succeeds in describing continuous as well as unbounded solution sets.
49 citations
Cites background from "Linear complementarity, linear and ..."
...An impressive collection of appl icat ions can be found in [12]....
[...]
01 Jan 2010
TL;DR: In this paper, a detailed discussion of optimization models in the natural gas industry, with the focus on natural gas production, transportation, and market, is given, and a detailed analysis of the optimization models is presented.
Abstract: With the surge of the global energy demand, natural gas plays an increasingly important role in the global energy market. To meet the demand, optimization techniques have been widely used in the natural gas industry, and has yielded a lot of promising results. In this chapter, we give a detailed discussion of optimization models in the natural gas industry, with the focus on the natural gas production, transportation, and market.
49 citations
TL;DR: Error bounds for the linear complementarity problem (LCP) are presented with the system matrix being an MB-matrix based on its equivalent LCP, from which some error bounds for LCP with special system matrices are derived.
Abstract: In this paper, we present error bounds for the linear complementarity problem (LCP) with the system matrix being an MB-matrix based on its equivalent LCP, from which some error bounds for LCP with special system matrices are derived. The numerical results show the sharpness of the proposed bounds.
49 citations
Cites background from "Linear complementarity, linear and ..."
...The LCP has various applications in the Nash equilibrium point of a bimatrix game, the contact problem and the free boundary problem for journal bearings (see [2, 5, 18]) etc....
[...]
TL;DR: The study of semi-complementarity problems can be used to prove new qualitative results applicable to the study of linear variational inequalities of the second kind.
Abstract: The main object of this paper is to present a general mathematical theory applicable to the study of a large class of linear variational inequalities arising in electronics. Our approach uses recession tools so as to define a new class of problems that we call “semi-complementarity problems”. Then we show that the study of semi-complementarity problems can be used to prove new qualitative results applicable to the study of linear variational inequalities of the second kind.
49 citations