运筹学学报
運籌學學報
운주학학보
OR TRANSACTIONS
2011年
2期
11-18
,共8页
数学规划%广义αη-单调性%广义αη-不变凸函数%仿射
數學規劃%廣義αη-單調性%廣義αη-不變凸函數%倣射
수학규화%엄의αη-단조성%엄의αη-불변철함수%방사
mathematical programming%generalized αη-monotonicity%generalized αη-invex functions%affine
用α和η关于第一分量是仿射的且是斜对称的条件代替条件C,得到如下结论:(1)如果一个函数的梯度是(严格)αη-伪单调的,则该函数是(严格)伪αη-不变凸的;(2)如果一个函数的梯度是拟αη-单调的,则该函数是拟αη-不变凸的.
用α和η關于第一分量是倣射的且是斜對稱的條件代替條件C,得到如下結論:(1)如果一箇函數的梯度是(嚴格)αη-偽單調的,則該函數是(嚴格)偽αη-不變凸的;(2)如果一箇函數的梯度是擬αη-單調的,則該函數是擬αη-不變凸的.
용α화η관우제일분량시방사적차시사대칭적조건대체조건C,득도여하결론:(1)여과일개함수적제도시(엄격)αη-위단조적,칙해함수시(엄격)위αη-불변철적;(2)여과일개함수적제도시의αη-단조적,칙해함수시의αη-불변철적.
If α and η are affine in the first argument and skew instead of Condition C, the following results are obtained: (i) if the gradient of a function is (strictly)αη-pseudomonotone, the function is (strictly) pseudo αη-invex; (ii) if the gradient of a function is quasi αη-monotone, the function is quasi αη-invex.
