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...produced from raw material A. There are two alternative paths of producing B from A. A mixed-integer nonlinear formulation is presented to solve the opt ...unt of chemical b purchased in external market b1: consumption of chemical b in process 1 c1: production capacity of chemical c in process 1

In T. A. Hauge, B. Lie, R. Ergon, M. D. Diez, G.-O. Kaasa, A. Dale, B. Glemmestad, and A Mjaavatten, editors, In Y. S. Abu-Mostafa, B. LeBaron, A. W. Lo, and A. S. Weigend, editors, ''Computational Finance (CF

toms a b f = a*sin(b);

\min\limits_{x} & f_{P}(x) & = & c^{T}x & \\s/t & {\hat A}x & = & b & \\& x & \geq & 0 & \max\limits_{y} & f_{D}(y) & = & b^{T}y \\s/t & {\hat A}^{T}y & \leq & c \\ & y

>> toms a b >> z = tomCmplx(a,b)

toms a b c cnbd = {a <= b <= c};

% b: y coordinate of center of circle toms a b r

cplex(c, A, x L, x U, b L, b U, cpxControl, callback, PriLev, Prob, IntVars, PI, SC, SI, sos1, |''b_U''||Upper bounds on the linear constraints. If empty, then ''b U''=''b L ''is assumed, i.e. equality constraints.

...\&\sum_{i=1}^m a_{ij} * x_{ij} \leq b_j~~,j=1,..,n\\&x \in B^{m \times n}, B=\{0,1\}.\\\end{array} [c, x L, x U, b L, b U, a, sos1] = abc2gap( A, b, C, SOS1);

x \in B^{m \times n}, B=\{0,1\}. [c, x L, x U, b L, b U, a, sos1] = abc2gap( A, b, C, SOS1);

...Inform, basis, lpiter, glnodes, iis, sa] = ... gurobi(c, A, x L, x U, b L, b U, grbControl, ...ces ==''> ''x(IntVars) are integers (if [], then no integers of type I or B are defined) GURONI checks which variables has x L=0 and x U=1, i.e. binary

...ck variables. To perform the numerical test, the residual vector ''r ''= ''b - Ax ''+ ''s ''is computed. If the largest component of ''r ''is judged to |0||The initial basis contains only slack variables: ''B ''= ''I ''.

...traints. For equality constraints (or fixed variables), set e.g. b L(k) == b U(k). |''QP.B''||Basis vector in TOMLAB QP standard.

<math> \frac{dx}{dt} = A*x + B*u </math> B = [0.538998 0 ... 0 0; 0 0 ... 0 0.634115]

...& \begin{array}{lcccl} 0& \leq & x & \leq & 1, \\ & & A x & = & b, \\ where <math>b=(600, 600)^T</math>,

...o} & 0 & \leq & x & \leq & x_{U} & \\& & & Ax & = & b, & ~x_{j} \in \mathbb{N}\, \forall j \in I \\ n}</math> and <math>b \in \mathbb{R}^{m}</math>. The variables <math>x \in I</math>, the index

6 (DETAILED) Detailed messages are reported. Like model size, con- tinuing B&B improvements. ...alue means that the depth is absolute. A negative value means a relative B&B depth. The "order" of a MIP problem is defined to be 2 times the number

[b,s] = size(rates); % banks/sites temp = reshape(temp,b,s)';

...ed as integers. If the input is empty ([ ]), then no integers of type I or B are defined. The interface routine ''cplex.m ''checks which of the integer |''QP.B''||Optimal active set, basis vector, in TOMLAB QP standard.

==Appendix B - The Matlab Interface Routines - Utility Routines== *[[Xpress Appendix B|Appendix B]]