By Knut Aas-Jakobsen, Mathis Grenacher (auth.)
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Extra info for Analysis of Slender Reinforced Concrete Frames
More specifically, the disjunctive conic cut gives the convex hull of the intersection between the disjunction x ≤ 1 ∨ x ≥ 2 and the feasible set of problem (18). This is not the case for the nonlinear conic mixed integer rounding inequality (20). 25). In particular, we can see that any of the cuts is enough to find the optimal solution. 25. Finally, we perform an additional test modifying the first constraint in (18) as follows: x + y + 2t = 8. In this case we use the disjunction x ≤ 2 ∨ x ≥ 3.
Let U = B ∩ N , then for any σ ∈ R we have that U ∩ (σ d0 + D) = 0. / This proves that the complement of C is open, thus C is closed. References 1. : Conic mixed-integer rounding cuts. Math. Program. 122(1), 1–20 (2010) 2. : Lifting for conic mixed-integer programming. Math. Program. A 126, 351–363 (2011) 3. : A conic integer programming approach to stochastic joint location-inventory problems. Oper. Res. 60(2), 366–381 (2012) Disjunctive Conic Cuts for Discrete Convex and Second-Order Conic Optimization 35 4.
Cs as1 as2 · · · ass b1 b2 · · · bs or, if the method is explicit, by the simplified tableau 0 c2 .. a21 .. . . . C. Butcher As examples, the Runge methods (5) and (6) have the tableaux 0 0 1 1 2 2 , 11 . 1 Taylor Expansion of the Exact Solution The analysis presented here is from , following the work of Gill  and Merson . To obtain a series for the exact solution, we need formulae for the second, third, . . , derivatives. These are easily found using the chain rule: y (x) = f (y(x)), y (x) = f (y(x))y (x) = f (y(x))f (y(x))), y (x) = f (y(x))(f (y(x)), y (x)) + f (y(x))f (y(x))y (x) = f (y(x))(f (y(x)), f (y(x))) + f (y(x))f (y(x))f (y(x)).
Analysis of Slender Reinforced Concrete Frames by Knut Aas-Jakobsen, Mathis Grenacher (auth.)