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  • SQOPT
    ...the ''basis matrix B ''is square and nonsingular. The elements of ''x<sub>B</sub> ''and ''x<sub>S</sub> ''are called the ''basic ''and ''superbasic ' ...t appears that no improvement can be made with the current definition of ''B'', ''S ''and ''N '', a nonbasic variable is selected to be added to ''S'',
    84 KB (13,939 words) - 14:15, 22 January 2012
  • SNOPT File Output
    If nonlinear constraints are present, the basis factorization ''B ''= ''LU ''is computed at the start of the first minor iteration. At this As columns of ''B ''are replaced during the minor iterations, LU may fluctuate up or down but
    49 KB (7,841 words) - 11:29, 14 August 2013
  • CPLEX cpxRetVec
    |''Index''||Result of CPLEX run. (S=Simplex, B=Barrier, MIP=Mixed-Integer) |20||(S,B) Solver method (1 = Primal, 2 = Dual, 4 = Barrier)
    9 KB (1,422 words) - 14:46, 19 March 2020
  • MINOS
    where the vectors ''b<sub>i</sub> '', ''c'', ''d'', ''l'', ''u ''and the matrices ''A<sub>i</sub> \min_{x,\ s}\ \ c^Tx \text{ subject to } Ax + s = b,
    27 KB (4,502 words) - 07:58, 14 August 2013
  • MINOS File Output
    ...determined by an LU factorization of the rectangular matrix ''BS ''= ( ''B S '')''<sup>T</sup>'' with stability being favored more than sparsity. |pivot||If column ''aq ''replaces the ''r''th column of the basis ''B'', pivot is the ''r''th element of a vector ''y ''satisfying ''By ''= ''aq
    50 KB (7,860 words) - 06:38, 7 September 2011
  • XA Solver Reference
    | | b<sub>L</sub> | | b<sub>U</sub>
    59 KB (8,573 words) - 06:05, 15 December 2010
  • Binbin2lin
    ''b''4 = ''b''1 ''* b''2. The problem should be built with the extra variable b4 in place of the ''b''4 ''<''= ''b''1
    1 KB (194 words) - 08:14, 10 January 2012
  • CPLEX cplexStatus
    |''Inform''||colspan="2"|Result of CPLEX run. (S=Simplex, B=Barrier, MIP=Mixed-Integer) |1||(S,B) Optimal solution is available
    5 KB (715 words) - 07:55, 15 August 2011
  • TomSym
    &gt;&gt; toms a b &gt;&gt; ezsolve(a^2 + 4*b^2 + 3*a - 2*b - a*b)
    5 KB (680 words) - 08:43, 11 August 2011
  • Xpress Appendix A
    ...inf, sinf, Inform, basis, lpiter, glnodes] = xpress(c, A, x L, x U, b L, b U, xpcontrol, callback, PriLev, Prob, IntVars, ...er bounds on the linear constraints. If empty, then ''b<sub>U</sub>'' = ''b<sub>L</sub>'' assumed.
    27 KB (4,166 words) - 13:28, 22 January 2012
  • TOMLAB Solving Least Squares and Parameter Estimation Problems
    b = x(1)-x(2); J = a * [ t.*e1+(e2-e1)*(1-1/b), -t.*e2+(e2-e1)/b, (e1-e2)/x(3) ];
    20 KB (3,073 words) - 10:18, 5 August 2014
  • TOMLAB
    ==Appendix B: Result - the Output Result Structure== *[[TOMLAB Appendix B|Appendix B: Result - the Output Result Structure]]
    12 KB (1,741 words) - 08:59, 13 August 2011
  • GENO
    |''QP.B''||Basis vector in TOMLAB QP standard. B. GENO Evolution
    45 KB (6,423 words) - 12:16, 17 December 2011
  • MINOS Solver Options
    ...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 be t ...ted accordingly. At most ''k ''updates are performed before the current ''B ''is factorized directly.
    17 KB (2,798 words) - 09:36, 14 August 2013
  • Xpress Test Routines in Tomlab Format
    Node 24: B&B integer solution found; objval -141278 Node 25: B&B integer solution found; objval -141056
    11 KB (1,409 words) - 13:26, 22 January 2012
  • SNOPT Description of the SQP method
    ...u ''and ''l ''as before. If the ''m × n ''matrix ''A ''and ''m''-vector ''b ''are defined as \end{array}\right) \quad and \quad b = \left(\begin{array}{c}
    9 KB (1,582 words) - 10:39, 14 August 2013
  • MipSolve
    ...r>''B''(''i'') = 0: Variable ''x''(''i'') is set on its lower bound. <br>''B''(''i'') = ''-''1: Variable ''x''(''i'') is set on its upper bound. ...lusion of variable x(i) in basic set. sum(B==1)==length(b) holds. See ''QP.B'' as input.
    10 KB (1,580 words) - 03:54, 20 August 2013
  • MINLP Solver Reference
    |''QP.B''||Basis vector in TOMLAB QP standard. ...traints. For equality constraints (or fixed variables), set e.g. b L(k) == b U(k).
    65 KB (9,880 words) - 10:07, 13 August 2013
  • TomSym Aircraft allocation under uncertain demand.
    Dantzig, G B, Chapter 28. In Linear Programming and Extensions. Princeton University Pre i: aircraft types and unassigned passengers (a, b, c, d)
    5 KB (482 words) - 09:32, 8 November 2011
  • CGO rbfSolve description
    \right\|_2 \right)+b^Tx + a, with <math>\lambda_1,\ldots,\lambda_n \in R</math>, <math>b \in R^d</math>, <math>a \in R</math> and <math>\phi</math> is either cubic
    27 KB (4,827 words) - 07:10, 4 March 2014
  • TomSym Structural Optimization of Process Flowsheets
    ...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
    3 KB (399 words) - 09:33, 8 November 2011
  • TOMLAB Introduction
    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
    8 KB (1,125 words) - 09:50, 15 July 2011
  • TOMLAB Defining Problems in TOMLAB
    toms a b f = a*sin(b);
    35 KB (5,335 words) - 05:57, 10 January 2012
  • DualSolve
    \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
    4 KB (631 words) - 08:09, 10 January 2012
  • TomCmplx
    &gt;&gt; toms a b &gt;&gt; z = tomCmplx(a,b)
    1 KB (188 words) - 10:12, 26 July 2011
  • PROPT
    toms a b c cnbd = {a <= b <= c};
    26 KB (4,044 words) - 03:27, 7 August 2014
  • TomSym Circle Enclosing Points - SNOPT Example
    % b: y coordinate of center of circle toms a b r
    2 KB (248 words) - 09:33, 8 November 2011
  • CPLEX cplex
    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.
    20 KB (3,274 words) - 07:46, 13 December 2011
  • CPLEX abc2gap
    ...\&\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);
    2 KB (287 words) - 11:17, 15 August 2011
  • Xpress Appendix B
    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);
    6 KB (963 words) - 08:39, 3 October 2011
  • GUROBI Appendix A
    ...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
    20 KB (3,108 words) - 06:07, 14 December 2011
  • SNOPT Optional parameters
    ...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 ''.
    50 KB (7,891 words) - 11:17, 14 August 2013
  • NLPQL
    ...traints. For equality constraints (or fixed variables), set e.g. b L(k) == b U(k). |''QP.B''||Basis vector in TOMLAB QP standard.
    25 KB (3,942 words) - 11:22, 17 December 2011
  • PROPT Linear Gas Absorber
    <math> \frac{dx}{dt} = A*x + B*u </math> B = [0.538998 0 ... 0 0; 0 0 ... 0 0.634115]
    3 KB (383 words) - 05:22, 14 February 2012
  • TOMLAB Solving Linear Quadratic and Integer Programming Problems
    ...& \begin{array}{lcccl} 0& \leq & x & \leq & 1, \\ & & A x & = & b, \\ where <math>b=(600, 600)^T</math>,
    18 KB (2,433 words) - 14:07, 14 January 2012
  • CutPlane
    ...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
    4 KB (593 words) - 08:09, 10 January 2012
  • MilpSolve
    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
    22 KB (3,382 words) - 10:58, 12 August 2014
  • Models Economics
    [b,s] = size(rates); % banks/sites temp = reshape(temp,b,s)';
    24 KB (2,900 words) - 19:00, 17 January 2012
  • CPLEX cplexTL
    ...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.
    21 KB (3,309 words) - 14:11, 21 January 2012
  • Xpress
    ==Appendix B - The Matlab Interface Routines - Utility Routines== *[[Xpress Appendix B|Appendix B]]
    3 KB (441 words) - 06:59, 28 September 2011
  • OQNLP
    |''QP.B''||Basis vector in TOMLAB QP standard. |''QP.B''||Basis vector in TOMLAB QP standard.
    51 KB (7,906 words) - 11:59, 22 January 2012
  • TomSym Optimal Feedback - A tomSym BMI demonstration
    ...bject to P >= 0 (LMI) (A+B*K)'*P+P*(A+B*K) <= -eye(2)-K'*K (BMI) B = [1;1];
    1 KB (151 words) - 09:32, 8 November 2011
  • TomSym MPC example with TomSym.
    B = [1;0]; nu = size(B,2); % Number of inputs
    4 KB (591 words) - 09:33, 8 November 2011
  • TomSym Ramsey Model of Optimal Economic Growth
    Murtagh, B, and Saunders, M A, A Projected Lagrangian Algorithm and its Implementation b = 0.25; % capital's value share
    3 KB (306 words) - 09:34, 8 November 2011
  • GUROBI
    ==Appendix B - The Matlab Interface Routines - Test Routines== *[[GUROBI Appendix B|Appendix B]]
    2 KB (261 words) - 04:11, 4 October 2011
  • SAL
    > mcc -B csharedlib:<lib-name> <m-files> <mex-files> > mcc -B cpplib:<library name> <m-files> <mex-files>
    25 KB (3,973 words) - 12:05, 21 January 2012
  • PdscoTL
    ...= ''&nabla;f ''(''x'') and ''x - x''1 = ''b<sub>L</sub> , x ''+ ''x''2 =''b<sub>U</sub>'', where ''x''<sub>1</sub> '', x''<sub>2</sub> ''> ''0. (''Pro {} & Ax & = & b. \\
    5 KB (794 words) - 08:17, 16 January 2012
  • CPLEX
    ==Appendix B: The Matlab Interface Routines - Utility Routines== * [[CPLEX Appendix B|Appendix B]]
    3 KB (476 words) - 08:52, 13 August 2011
  • Improving the speed of tomSym
    ...ewrite the objective as <tt>sum(x.^2)</tt> and add the constraint <tt>A*x==b</tt>. This formulation gives much more information to the solver, and avoid ...==1</tt> don't work well with numeric solvers, because <tt>a</tt> and <tt>b</tt> will have very different magnitudes in the solution.
    5 KB (812 words) - 10:25, 26 July 2011
  • PROPT Multiphase Aircraft Trajectory Planning Example
    b = a*(1-1/flinv); % semi-minor axis rm = @(phi) (a.^2.*b.^2)./((a.*cos(phi)).^2+(b.*sin(phi)).^2).^(3/2);
    6 KB (912 words) - 05:34, 14 February 2012
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