Convex Inequalities Without Constraint Qualification nor Closedness Condition, and Their Applications in Optimization
نویسندگان
چکیده
منابع مشابه
Convex Inequalities without Constraint Qualification nor Closedness Condition, and Their Applications in Optimization
Given two convex lower semicontinuous extended real valued functions F and h de ned on locally convex spaces, we provide a dual transcription of the relation
متن کاملDuality without constraint qualification in nonsmooth optimization
We are concerned with a nonsmooth multiobjective optimization problem with inequality constraints. In order to obtain our main results, we give the definitions of the generalized convex functions based on the generalized directional derivative. Under the above generalized convexity assumptions, sufficient and necessary conditions for optimality are given without the need of a constraint qualifi...
متن کاملA closedness condition and its applications to DC programs with convex constraints
This paper concerns a closedness condition called (CC), requiring a convex function and a convex constrained system. This type of condition has played an important role in the study of convex optimization problems. Our aim is to establish several characterizations of this condition and to apply them to study minimizing problems involving a DC function under a cone-convex constraint and a set co...
متن کاملOn Constraint Qualification for an Infinite System of Convex Inequalities in a Banach Space
For a general infinite system of convex inequalities in a Banach space, we study the basic constraint qualification and its relationship with other fundamental concepts, including various versions of conditions of Slater type, the Mangasarian–Fromovitz constraint qualification, as well as the Pshenichnyi–Levin–Valadier property introduced by Li, Nahak, and Singer. Applications are given in the ...
متن کاملClosedness Type Regularity Conditions in Convex Optimization and Beyond
The closedness type regularity conditions have proven during the last decade to be viable alternatives to their more restrictive interiority type counterparts, in both convex optimization and different areas where it was successfully applied. In this review article we deand reconstruct some closedness type regularity conditions formulated by means of epigraphs and subdifferentials, respectively...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Set-Valued and Variational Analysis
سال: 2010
ISSN: 1877-0533,1877-0541
DOI: 10.1007/s11228-010-0166-4