ISSN:
1573-2878
Keywords:
Efficient sets
;
penalty functions
;
point convergence
;
set convergence
;
limit sets
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract This paper generalizes the penalty function method of Zang-will for scalar problems to vector problems. The vector penalty function takes the form $$g(x,\lambda ) = f(x) + \lambda ^{ - 1} P(x)e,$$ wheree ⊀R m, with each component equal to unity;f:R n →R m, represents them objective functions {f i} defined onX $$ \subseteq $$ R n; λ ∈R 1, λ〉0;P:R n →R 1 X $$ \subseteq $$ Z $$ \subseteq $$ R n,P(x)≦0, ∨x ∈R n,P(x) = 0 ⇄x ∈X. The paper studies properties of {E (Z, λ r )} for a sequence of positive {λ r } converging to 0 in relationship toE(X), whereE(Z, λ r ) is the efficient set ofZ with respect tog(·, λr) andE(X) is the efficient set ofX with respect tof. It is seen that some of Zangwill's results do not hold for the vector problem. In addition, some new results are given.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF00935007
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