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- Title
SEARCH FOR THE PARETO POINT BASED ON THE MAXIMIN PRINCIPLE OF IMPROVEMENT RATES OF OBJECTIVE FUNCTIONS.
- Authors
Tauts, A.; Krumm, L.
- Abstract
The aim of this paper is to find the Pareto point for the numerical value of objective functions F1,...Fn(x) with the argument x belonging to a certain Hilbert space. Starting from a fixed point x0, the optimization trajectory is chosen in such a way that on every step the improvement rate of the value of the slowest improvement of the objective function be possibly great. It is proved that on every step one has to choose the non-negative coefficients α1,...αn with the constraint ∑αi=αi=1, so that the norm of the gradient of the function ∑αi=iFi(x) is minimal, and then to make the next step in the direction of the chosen gradient.
- Subjects
HILBERT space; BANACH spaces; SPACE trajectories; HYPERSPACE; ASTRODYNAMICS
- Publication
Oil Shale, 2005, Vol 22, Issue 2, p197
- ISSN
0208-189X
- Publication type
Article