简介：

简介：Marginalriskrepresentstheriskcontributionofanindividualassettotheriskoftheentireportfolio.Inthispaper,weinvestigatetheportfolioselectionproblemwithdirectmarginalriskcontrolinalinearconicprogrammingframework.'Theoptimizationmodelinvolvedisanonconvexquadraticallyconstrainedquadraticprogramming(QCQP)problem.WefirsttransformtheQCQPproblemintoalinearconicprogrammingproblem,andthenapproximatetheproblembysemidefiniteprogramming(SDP)relaxationproblemsoversomesubrectangles.InordertoimprovethelowerboundsobtainedfromtheSDPrelaxationproblems,linearandquadraticpolarcutsareintroducedfordesigningabranch-and-cutalgorithm,thatmayyieldane-optimalglobalsolution(withrespecttofeasibilityandoptimality)inafinitenumberofiterations.ByexploringthespecialstructureoftheSDPrelaxationproblems,anadaptivebranch-and-cutruleisemployedtospeedupthecomputation.Theproposedalgorithmistestedandcomparedwithaknownmethodintheliteratureforportfolioselectionproblemswithhundredsofassetsandtensofmarginalriskcontrolconstraints.

简介：这篇文章调查与家庭安装时间安排的相同平行机器。是结束的加权的和预定的客观功能，这个问题被知道强烈NP难。我们建议一个建设性的启发式的算法和三互补更低的界限。二这些界限由安装时间的消除或由散布他们中的每到相应家庭的工作继续，当第三基于lagrangian松驰时。界限并且启发式被合并到一个branch-and-bound算法。获得的试验性的结果在以前的工作介绍的方法超过那些，以解决的问题的尺寸。