ISSN:
1573-2878
Keywords:
Efficient sets
;
ε-efficiency
;
weighting factors
;
constrained objectives
;
penalty functions
;
ideal points
;
Markov decision processes
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract This paper considers the extension of ε-optimality for scalar problems to vector maximization problems, or efficiency problems, which havem objective functions defined on a set $$X \subseteq \mathbb{R}^n $$ . It is shown that the natural extension of the scalar ε-optimality concepts [viz, given ε〉0, given a solution setS, ifx∈S there exists an efficient solutiony with ∥f(x)−f(y)∥≦ε, and given an efficient solutiony, there exists anx∈S with ∥f(x)−f(y)∥≦ε] do not hold for some methods used. Six concepts of ε-efficient sets are introduced and examined, to a very limited extent, in the context of five methods used for generating efficient points or near efficient points. In doing so, a distinction is drawn between methods in which the surrogate optimizations are carried out exactly, and those where terminal ε-optimal solutions are obtained.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF00940762
Permalink
