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&.',* and CI::;, are a 1 x (i - 1) row vector variable and a 1 x (j -1) row vector variable, whose
components weight duai proposais from the corresponding lower bound subproblem at level
II in the subprablem of part 2 and 4. respectively.
x:" is an n, x(k-1) mauix andyf-' is a r, x (k-1) mauix. i.e. x:-'= (x!. .r,'. ... . .$') and
y:-'= . .. , y:-'), coming from the fint (k-1) primal solutions of subproblem r. ~3.4.
xi1 is a n2 x(i-1) matrix and y:' is a rz x (i-1) mauix. i.e. x;' = (2:. xi. . . . . .&') and
Y;' = ($. $. . . . . - YI'), _ coming from the first (i-1) prima1 solutions of subproblem 2. At the
start of each iteration k. i is reset to i=l and. x!' and y;' are met to nul1 matrices.
Y:-' = (4:. Yi. . . . . y:-') . coming from the fint (i-1) prima1 solutions of subproblem 4. At the
stvt of each itention k. j is reset ro j= 1 and. xi" and y:.' are reset to nul1 matrices.
n:-' is a (k-I) xm, rnatrix and&' is a (k-1) x q, matrix. Le. n:-'= (dr
. +r. . . . . d'Ir )'
and ak-' = (di, &', . . . . d-lr )r . coming from the fint (k-1) dual solutions of subproblem r.
r=l. 2.
ni-' is a (i- 1) xmi matrix and^;.' is a (i- L) x 41 mûtrix, i.e. ni-' = (dr . $r. . . . . d-'' Ir
and = (dr .&. . . . d-lr )' . corning from the fint (i-1) dual solutions of subproblem 1.
At the start of each itention k, i is reset to i=l and. ni" and QI-' are met to nuIl matrices.
and ~j-' = (dr . . . . &-lr )T . coming from the fint (i-1) dual solutions of subproblern 3.
At the stm of each iteration k. j is reset tokl and ni" lurd ni'' are met to nul1 matrices.
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