Well-posedness In Constrained Vector Optimization

Well-posedness plays a crucial role in stability theory and in establishing convergence of algorithms for optimization problems. This topic has been widely studied in different fields of scalar optimization such as mathematical programming, calculus of variations and optimal control, etc.. Recently, vector optimization theory has been intensively developed. Many researchers have tried to study well-posedness in vector optimization. In this thesis, combining the idea of well-posednesses used in Miglierina and Molho [7], Lordian [14] and Bednarczuch [3] with that of Huang and Yang [19], we define type I(II) generalized pointwise L-well -posedness , type I(II) generalized pointwise M-well-posedness ,(weakly) type I generalized pointwise B-well-posedness and (weakly) type II generalized pointwise B-well-posedness as well as type I(II) generalized global M-well-posedness, type I(II) generalized global M-well-posedness, (weakly) type I generalized global B-well-posedness and (weakly) type II generalized global B-well-posedness for the constrained vector optimizationprblem: (where f and g are continuous ). Various criteria and characterizations for these types of well-posedness are given and their relationships are investigated.