摘要
众所周知,最优性条件的讨论在最优化理论中占有十分重要的地位,尤其是带约束的一般的极值问题(P)的高阶最优性条件的讨论更引人注目,例如 K.H.Hoffman andH.J.Cornstaedt及A.Linnemann借助于高阶变分集合;F.Lempio and J.Zowem利用像空间中的高阶凸逼近; B.
The paper proposes some new concepts of higher order feasible (descent) directions,higher order quasifeasible (quasidescent) directions and higher order tangent directions;Using the support functions of these sets of higher order directions, higher order necessaryconditions for nonsmooth optimal problem (P) in topological vector spaces are established. Theabove set's equivalent presentation and the relations between the sets and the higher ordervariational sets in [1-3] are discussed under Frechet differentiability assumptions, with theresults higher order necessary conditions for smooth optimal problems (Th 4.2) are obtainedwhich extend nearly all the higher and lower order optimality necessary conditions for smoothproblems in [1-9], [12-15].
出处
《应用数学学报》
CSCD
北大核心
1990年第2期156-167,共12页
Acta Mathematicae Applicatae Sinica
