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
TL;DR: This paper introduces a novel randomized method of solving LP problems by moving along the facets and within the interior of the polytope along rays randomly sampled from the polyhedral cones defined by the bounding constraints.
Abstract: Linear programming (LP) problems are commonly used in analysis and resource allocation, frequently surfacing as approximations to more difficult problems. Existing approaches to LP have been dominated by a small group of methods, and randomized algorithms have not enjoyed popularity in practice. This paper introduces a novel randomized method of solving LP problems by moving along the facets and within the interior of the polytope along rays randomly sampled from the polyhedral cones defined by the bounding constraints. This conic sampling method is then applied to randomly sampled LPs, and its runtime performance is shown to compare favorably to the simplex and primal affine-scaling algorithms, especially on polytopes with certain characteristics. The conic sampling method is then adapted and applied to solve a certain quadratic program, which compute a projection onto a polytope; the proposed method is shown to outperform the proprietary software Mathematica on large, sparse QP problems constructed from mass spectometry-based proteomics.
4 citations
Cites methods from "Linear complementarity, linear and ..."
...One such approach is the geometrically motivated gravity descent method [10], which simulates the descent of a very small (radius [) sphere of ‘‘mercury’’ to the minimum of the polytope....
[...]
16 Mar 2016
TL;DR: This work casts the interactions between mobile users and wireless providers as a two-stage Stackelberg game, which establishes the existence and uniqueness of a link demand equilibrium (LDE) under certain conditions, and develops a recursive back-tracking algorithm to find the PE.
Abstract: The rapidly growing popularity of online social services has greatly spurred mobile users' online social interactions, which in turn has boosted their demand for data usage. However, wireless service providers' revenue growth is constrained by the capacity of the physical network infrastructure, and is further challenged by the price competition among different wireless providers. To fully understand the potential benefit brought by social services, we study mobile users' data usage behavior subject to social network effect in the social domain and congestion effect in the physical wireless domain, based on which we explore wireless providers' pricing strategies under competition. In particular, we cast the interactions between mobile users and wireless providers as a two-stage Stackelberg game: In Stage I, each provider decides its pricing strategy to maximize its revenue in competition with other providers' pricing strategies; In Stage II, given the providers' pricing strategies, users choose data usage subject to both social network effect and congestion effects. We analyze the two-stage game using backward induction. For Stage II, we establish the existence and uniqueness of a link demand equilibrium (LDE) under certain conditions. For Stage II, we establish the existence of a mixed strategy pricing equilibrium (PE), and further develop a recursive back-tracking algorithm to find the PE. Our results provide insight on the impact of wireless providers' competition on their revenues.
4 citations
Additional excerpts
...To address the challenge in analyzing the game in Stage II due to the multidimensional strategy space of each user, the data usage problem among users is cast as a game played by virtual players (links connecting each user and each provider)....
[...]
01 Jan 2011
TL;DR: A survey of recent results in computer science related to the computation of fixed points can be found in this article, with the central one being that the problem of fin ding an approximate Nash equilibrium of a bimatrix game is PPAD-complete.
Abstract: This is an expository survey of recent results in computer science related to the computation of fixed points, with the central one being that the problem of fin ding an approximate Nash equilibrium of a bimatrix game is PPAD-complete. This means that this problem is, in a certain sense, as hard as any fixed point problem. Subsequently many other problems have been shown to be PPADcomplete, including finding Walrasian equilibria in certai n simple exchange economies. We also comment on the scientific consequences of complexity as a bar rier to equilibration, and other sorts of complexity, for our understanding of how markets operate. It is argued that trading in complex systems of markets should be analogized to games such as chess, go, bridge, and poker, in which the very best players are much better than all but a small number of competitors. These traders make positive rents, and their presence is a marker of complexity. Consequences for the efficient markets hypothesis are sketched.
4 citations
Additional excerpts
...(Cf. Murty (1988) and Cottle et al. (1992).)...
[...]
TL;DR: This issue is focused on latest research results in wireless sensor networks (WSNs) that address key issues related to high-confidence cyber-physical systems and applications that address the need for coupling geographically distributed computing devices with physical elements.
Abstract: Technical advances in ubiquitous sensing, embedded computing, and wireless communication are leading to a new generation of engineered systems called cyber-physical systems (CPS). This field is attracting more and more attention from researchers, practitioners, as well as the governments. Technically, cyber-physical systems are integrations of computation, networking, and physical dynamics, in which embedded devices are massively networked to sense, monitor and control the physical world. CPS has been regarded as the next computing revolution. This revolution will be featured by the envisioned transform that CPS will make on how we interact with the physical world. To facilitate unprecedented interactions between human beings and the physical world, sensor networks will become a crucial ingredient of CPS due to the need for coupling geographically distributed computing devices with physical elements. The proliferation of affordable sensor network technologies has significantly contributed to recent progress in CPS. On the other hand, the unique features of CPS (e.g. cyber-physical coupling driven by new demands and applications) give rise to a lot of open challenges for design and deployment of sensor networks in such systems. In particular, high-confidence CPS requires the employed sensor networks to support real-time, dependable, safe, secure, and efficient operations. In this issue we are focused on latest research results in wireless sensor networks (WSNs) that address key issues related to high-confidence cyber-physical systems and applications. In response to our call-for-papers, we have received 36 submissions, out of which 15 papers are finally accepted as a result of thorough review process by international experts in respective areas. The selection provides a glimpse of the state-of-the-art research in the field. In the paper "A Game Theoretic Approach for Interuser Interference Reduction in Body Sensor Networks", Wu et al present a decentralized inter-user interference reduction scheme with non-cooperative game for body sensor networks (BSNs). A no-regret learning algorithm for reducing the effect of the inter-user interference with low power consumption is proposed. The correctness and effectiveness of the proposed scheme are theoretically proved, and experimental results demonstrate that the effect of inter-user interference can be reduced effectively with low power consumption.
4 citations
TL;DR: In this article, the convergence of the MGSTS iteration method is studied in detail for solving a class of linear complementarity problems with the system matrix either being an H+-matrix with non-positive off-diagonal entries or a symmetric positive definite matrix.
Abstract: Inthis paper, amodulus-basedgeneralizedskew-Hermitiantriangularsplit- ting (MGSTS) iteration method is present for solving a class of linear complemen- tarity problems with the system matrix either being an H+-matrix with non-positive off-diagonal entries or a symmetric positive definite matrix. The convergence of the MGSTS iteration method is studied in detail. By choosing differentparameters, a series of existing and new iterative methods arederived, including the modulus-based Jacobi (MJ) and the modulus-based Gauss-Seidel (MGS) iteration methods and so on. Exper- imental results are given to show the effectiveness and feasibility of the new method when it is employed for solving this class of linear complementarity problems.
4 citations
Cites background from "Linear complementarity, linear and ..."
...For more details, see [6, 17, 19] and the references therein....
[...]