Research On Global Optimality Conditions, Algorithms And Applications Of Quadratic Programming

Quadratic programming has been worth study as a kind of nonlinearprogramming, because it could not only be used to solve practical problems such asengineering design, production scheduling and market economy, and a lot ofnonlinear problem can be converted into this kind of problem. So discussion on thegeneral quadric programming problem, from both theory and practice, can not onlyhelp people deal with practical problems, but also contribute to theoretical research.This article discusses the problem mainly from the three aspects, which areapplications, the optimality conditions and algorithms. The main research methodconsists of sum-up, theoretical derivation and innovative thinking, etc. Applicationsin reality of quadratic programming within different fields are summarized in thispaper. Through modeling and analyzing, knowledge of quadratic programming isenhanced, and alternatives to solve these practical problems are introduced. Becauseof variety of quadratic programming model, different models are classified accordingto the objective function and constraints, and corresponding optimality conditions aregiven for each category of quadratic programming. Among the optimality conditions,some are proposed by researchers, some are transformed from other problems, andsome are obtained from continuous research.Quadratic programming is a broad class of problems, and kinds ofalgorithms have been proposed. So it is unrealistic to summarize all thesealgorithms. This article makes some discussions from the optimizedimprovement strategies and problem solving skill. Different optimizationimprovement strategies induce different algorithms, while the orientation ofthe concrete processing skill determines the algorithm’s accuracy. The interiorpoint algorithms are discussed in detail as a specific algorithm for quadraticprogramming problem. Because this paper contributes more to the theoreticalstudy, it ends up with an application in the portfolio selection problem.Finally some research topics are proposed.