The existence of minimum points for a real function f over a closed and unbounded set D is analyzed, focusing on the behavior of f along the so called recession directions of D. With this regard several new coercivity concepts are introduced together with an extension of the recession function. Relationships between coercivity and the behavior of the introduced recession function are studied, giving particular attention to their fundamental role in deriving optimality conditions. Necessary and sufficient conditions guaranteeing the existence of the minimum points are given as well as results related to the boundedness of the set of optimal solutions.
Coercivity Concepts and Recession Function in Constrained Problems
CAMBINI, RICCARDO;CAROSI, LAURA
2003-01-01
Abstract
The existence of minimum points for a real function f over a closed and unbounded set D is analyzed, focusing on the behavior of f along the so called recession directions of D. With this regard several new coercivity concepts are introduced together with an extension of the recession function. Relationships between coercivity and the behavior of the introduced recession function are studied, giving particular attention to their fundamental role in deriving optimality conditions. Necessary and sufficient conditions guaranteeing the existence of the minimum points are given as well as results related to the boundedness of the set of optimal solutions.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.