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Table 1 Dimensions of the resulting non-linear programming problems

From: Dynamic estimation of specific fluxes in metabolic networks using non-linear dynamic optimization

Variables  
Differential state variables p x 4·(n time−1)·(m ext+1)
Algebraic state variables p z 4·(n time−1)·n irr
Spline parameters p u n g+d·(k+1)
Internal knot locations t knot n g
Initial values x 0 m ext+1
K matrix values n·d
Equality constraints  
Differential state collocation constraints 3·(n time−1)·(m ext+1)
Differential state continuity constraints (n time−2)·(m ext+1)
Algebraic state collocation constraints (3·(n time−1)+1)·n irr
Algebraic state continuity constraints (n time−2)·(n irr)
Initial value constraints m ext+1
K null space constraints m int·d
K orthogonality constraints d · ( d + 1 ) 2