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А.А. Грешилов
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Ill-posed problems and multicriteria programming
© A.A. Greshilov
Bauman Moscow State Technical University, Moscow, 105005, Russia
Solving ill-posed problems by methods of multicriteria mathematical programming has
been considered. Several methods of multicriteria mathematical programming (method of
compression of acceptance region and goal programming) are used simultaneously al-
lowing considering additional types of restrictions (nonnegativity of the solution, bound-
edness of solution) which must be met by evaluation of solution and which do not require
definition of the regularization parameters necessary in the classical methods of regular-
ization. When registering a small number of isotopes the merger of the two types of ura-
nium- 235 instant fission into one kind of division and two types of plutonium-239 fission
into one kind of division is used. Simultaneously different variants of the nuclear explo-
sion mechanism are considered. Determination of contributions of different fission kinds
into the total activity of isotopes of krypton and xenon is performed by formation of a
functional for a given moment of separation
q
t
and time measurements t of functions
l
F
.
They are obtained from the functional by its differentiation on the elements
j
N
of the
system of linear algebraic equations (SLAE) at fixed values of the specific activity
( , ).
true
ij
q
a t t
Solving SLAE is performed by generating multiple objective functions and
using the 4 methods of multicriteria mathematical programming, reducing multicriteria
problem to one-criterion problem with constraints. The solutions of the mentioned one-
criterion problem with constraints are obtained by the iterative computational proce-
dures with the given specific activity
( , )
true
ij
q
a t t
and when its assessment was specified
for each iteration. The point estimates of the contributions of different fission kinds into
the total activity of isotopes are determined. For definition of the moment of separation
q
t
contributions
j
N
are calculated for different values
q
t
and the value at which the
ratio
2
2
true
1
1
1
,
/
n
m
m
i
ij
q
j
j
i
j
j
A t
a t t
N
N
is minimal is chosen.
Keywords:
regularization methods, fission products, nuclear explosion, separation of
isotopes, multicriteria programming, targeted programming, compression method, itera-
tive method of solving
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