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Date: Tue, 05 Nov 1996 21:04:54 GMTServer: NCSA/1.5Content-type: text/htmlLast-modified: Fri, 10 Nov 1995 18:14:32 GMTContent-length: 6945<HTML><HEAD><TITLE>ICCP 95: Meeting Report</TITLE></HEAD><BODY><H1>ICCP 95: Meeting Report</H1><UL>The first international conference on complementarity problems washeld at the Johns Hopkins University in Baltimore from November 1-4,1995. The meeting was attended by over 50 researchers from around theworld, including attendees from Australia, Belgium, Canada, the CzechRepublic, Denmark, Finland, Germany, Great Britain, India, Italy,Japan, the Netherlands, Norway, Portugal, Sweden and the UnitedStates. The meeting was organized with the aim of bringing togetherresearchers of the mathematical programming aspects ofcomplementarity problems and experts in a variety of applicationsareas. The purpose of the meeting was to create increased crossfertilization and communication between these areas. In particular,a better understanding and appreciation of the differentaspects that each of these areas considers is expected to bebeneficial for the effective solution of practical complementarity problems arising from applied disciplines. As such, we believe that the meeting was a great success.<p>With more than three decades of research, the subject of complementarity problems has become a well-establishedand fruitful discipline within mathematical programming. Sources of complementarity problems are diverse and includemany problems in engineering, economics, and the sciences.Several monographs and surveys have documented the basic theory,algorithms, and applications of complementarity problems and theirrole in optimization theory.<p>The meeting started with an overview of the complementarity field atwhich stage a new web site, CPNET, http://www.cs.wisc.edu/cpnet/was announced. When completed, this site will eventually contain up-to-date information on upcoming conferences in the area, a list of active researchers and pointers to work on algorithms, applications and software.<p>Currently, the page contains a list of all the researchers present at the conference, along with papers and software that outline somedevelopments in the area. This includes the growing collection of testproblems for MCP, MCPLIB, and the COMPLEMENTARITY TOOLBOX, a suite ofprograms and routines for use in conjunction with MATLAB. It is hopedthat CPNET will allow this collection to grow considerably to includemany new algorithms and application problems. There are some pointersto extensions of modeling software that allow real applications to beformulated in standard modeling languages.<p>There were various themes that developed during the meeting. Severalspeakers introduced new extensions of the basic framework, and citedapplications that needed such extensions. Some new theoreticalresults were outlined relating to vertical, horizontal and extendedlinear complementarity problems, along with several ideas to unifythese areas. Other speakers considered noncooperative and stochasticgame theory and outlined existence results and algorithms for theirsolution. Variational and bimatrix inequalities also drew theattention of several talks. Merit functions and smoothing techniqueswere also popular topics.<p>One extension that received considerable attention was the MathematicalProgram with Equilibrium Constraints (MPEC). Several algorithms weregiven for the solution of these problems, and lots of discussionresulted during application talks relating to reformulating problemsinto this framework. This appears to be a very fruitful area forfuture research.<p>Contact problems are a rich source of complementarity problems. For these problems, complementarity is the result of the contactcondition which stipulates that the gap between two objects incontact is either zero or the pressure between them is zero.Classical obstacle problems were extended to include the effects ofconvection and diffusion. An interesting use of complementarity incontact mechanics arises in robot design and key features of theproblem that can be modeled in the new framework include sliding,friction and rigid body properties.Structural mechanics has also used complementarity models in studiesof material elasticity and plasticity. Several very informative and interesting talks opened up these areas to the field in general.<p>Complementarity has been used in economics for a long time. Therenowned Walrasian law of supply and demand in general equilibriumtheory states that either there is excess supply or the price of thecorresponding good is zero. Several extensions of this basic ideawere outlined in talks that dealt with oligopolistic equilibria,integrated assessment for problems in energy modeling, relocationeffects due to the European Common Market and the National EnergyModeling System (NEMS). The use of similar models for trafficassignment was also outlined. In this area, dynamic models arebecoming important and several new ideas for tolling and congestionanalysis were presented at the meeting.<p>Several new algorithmic developments were outlined at the meeting.Some of these involved the traditional simplicial and pivotal basedtechniques while others used novel reformulations of thecomplementarity problem both as smooth and nonsmooth systems ofnonlinear equations. A very popular approach takes systems ofnonsmooth equations and applies a smoothing so that traditional Newtonbased techniques could be applied. Still other methods were based onquadratic programming and proximal points formulations. Newcomputational extensions were also outlined.Several talks introduced new merit functions that will prove useful inerror analysis and future algorithmic design.<p>In conclusion, the meeting showed that the field of complementarityresearch is a burgeoning area. There are already many interesting algorithms for solving complementarity problems, along with fairlysophisticated techniques for analysis and computation. The growth in the number of new application areas that use this framework will require even more sophisticated solution techniques. Furthermore, it is clear that even more applications will be developedthat use complementarity modeling in some form or another, a significant portion of which was made possible by this meeting.<p>A refereed proceedings of this meeting will be published in 1996 bySIAM. Further developments in this area will undoubtedly be reportedat the next International Conference on Complementarity Problems.Planning is already under way and the conference is tentatively set for July 1998 to be held in Madison, Wisconsin.</UL><HR><ADDRESS> Michael Ferris <br> Computer Sciences Department <br> University of Wisconsin, Madison <br> ferris@cs.wisc.edu <br><p> Jong-Shi Pang <br> Department of Mathematical Sciences <br> The Johns Hopkins University, Baltimore <br> jsp@vicp.mts.jhu.edu <br></ADDRESS></BODY></HTML>⌨️ 快捷键说明
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