简介：在这篇论文我们在场为解决LC1的一个filter-trust-region算法使用第二Dini的非强迫的优化问题上面的方向性的衍生物。我们在合理假设下面建立算法的全球集中。

简介：TheauthorsintroduceandinvestigatetheT_C-Gorensteinprojective,L_CGorensteininjectiveandH_C-GorensteinflatmoduleswithrespecttoasemidualizingmoduleCwhichsharesthecommonpropertieswiththeGorensteinprojective,injectiveandflatmodules,respectively.TheauthorsprovethattheclassesofalltheT_C-GorensteinprojectiveortheH_C-GorensteinflatmodulesaxeexactlythoseGorensteinprojectiveorfiatmoduleswhichareintheAuslanderclasswithrespecttoC,respectively,andtheclassesofalltheL_C-GorensteininjectivemodulesaxeexactlythoseGorensteininjectivemoduleswhichareintheBassclass,sotheauthorsgettherelationsbetweentheGorensteinprojective,injectiveorflatmodulesandtheC-Gorensteinprojective,injectiveorflatmodules.Moreover,theauthorsconsidertheT_C(R)-projectiveandL_C(R)-injectivedimensionsandT_C(R)-precoversandL_C(R)-preenvelopes.Finally,theauthorsstudytheH_C-GorensteinflatmodulesandextendtheFoxbyequivalences.