TY - JOUR
T1 - Multi-objective infinite programming
AU - de Oliveira, Valeriano Antunes
AU - Rojas-Medar, Marko Antonio
PY - 2008/5
Y1 - 2008/5
N2 - Using the theory of abstract optimization problems in infinite-dimensional spaces we provide necessary optimality conditions of first and second order for weakly efficient solutions of the multi-objective infinite programming problem. Sufficient conditions are given under invexity assumptions. We generalize the notion of KKT-invexity for the multi-objective infinite problem and show that this notion is a necessary and sufficient condition for every vector KKT solution to be a weakly efficient solution. Moreover, we develop a theorem of the alternative, useful for proving some of our results.
AB - Using the theory of abstract optimization problems in infinite-dimensional spaces we provide necessary optimality conditions of first and second order for weakly efficient solutions of the multi-objective infinite programming problem. Sufficient conditions are given under invexity assumptions. We generalize the notion of KKT-invexity for the multi-objective infinite problem and show that this notion is a necessary and sufficient condition for every vector KKT solution to be a weakly efficient solution. Moreover, we develop a theorem of the alternative, useful for proving some of our results.
KW - Infinite programming problems
KW - Invexity
KW - KKT-invexity
KW - Multi-objective optimization
KW - Weakly efficient solutions
UR - https://www.scopus.com/pages/publications/41149087624
U2 - 10.1016/j.camwa.2007.08.029
DO - 10.1016/j.camwa.2007.08.029
M3 - Article
AN - SCOPUS:41149087624
SN - 0898-1221
VL - 55
SP - 1907
EP - 1922
JO - Computers and Mathematics with Applications
JF - Computers and Mathematics with Applications
IS - 9
ER -