Sentence examples for th constraint from inspiring English sources

Where: g i is the i th constraint.

In particular, for all we replace the th constraint in (21d) by (22).

f n (ϕ k ) is the n th constraint of the original minimax problem at a solution point ϕ k.

For the i th constraint, the auxiliary problem (34 36) is shown as follows: { hbox{max} }begin{array}{*{20}l} hfill end{array} sumlimits_{{j in J_{i} }} {hat{a}_{ij} eta_{ij} left| {x_{j} } right|} (34) {text{s}}.

G(d l ) = A d l - a is the matrix represents the constraint of the QP sub-problem at a solution point d l and g n (d l ) is the n th constraint.

Open image in new window C j 0 i and C ri are positive real numbers ∀ j, r, i, and a k 0 i, a ki are real numbers ∀ k, i. Open image in new window P j 0 = Number of terms present in j 0 th objective function, Open image in new window P r = Number of terms present in r th constraint, Open image in new window C r = Boundary value of r th constraint, Open image in new window.

The ∇f n (ϕ k ) is the gradient of n th constraints at the k th major iteration.

f m (x) is the m-th objective, g i (x) is the i-th constraint inequality and h j (x) is the j-th constraint equation.

(1) Eleft[ {fleft( {varvec{x},varvec{xi}} right)} right] = int {fleft( {varvec{x},varvec{xi}} right)phi left varvec{xi}right)} {text{d}}varvec{xi} (2 where (varvec{x}) is the decision vector; ξ denotes fuzzy stochastic vector; E is the expected value operator; g j denotes the j-th constraint.

Specifically, in the original problem, by removing the k-th row and k-th column of the matrix P H in (8), the k-th constraint in (9b), and the elements related with π k in (9a) and (9d), the optimal solution is not changed.

In addition, the degree of violation value of solution x from k-th constraint G k (x) is defined as G_{k} (varvec{x}) = left{ {begin{array}{*{20}l} {hbox{max} { 0,g_{k} (varvec{x})},quad k = 1,2, cdots,q,} hfill {hbox{max} { 0,left| {h_{k} (varvec{x})} right| - delta },quad k = q + 1,q + 2, cdots,m.} hfill end{array} } right.