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  • ...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
  • 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
  • |''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
  • 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
  • ...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
  • | | b<sub>L</sub> | | b<sub>U</sub>
    59 KB (8,573 words) - 06:05, 15 December 2010
  • ''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
  • |''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
  • &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
  • ...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
  • 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
  • ==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
  • |''QP.B''||Basis vector in TOMLAB QP standard. B. GENO Evolution
    45 KB (6,423 words) - 12:16, 17 December 2011
  • ...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
  • 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
  • ...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
  • ...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
  • |''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
  • 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
  • \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
  • ...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
  • 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
  • toms a b f = a*sin(b);
    35 KB (5,335 words) - 05:57, 10 January 2012
  • \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
  • &gt;&gt; toms a b &gt;&gt; z = tomCmplx(a,b)
    1 KB (188 words) - 10:12, 26 July 2011
  • toms a b c cnbd = {a <= b <= c};
    26 KB (4,044 words) - 03:27, 7 August 2014
  • % b: y coordinate of center of circle toms a b r
    2 KB (248 words) - 09:33, 8 November 2011
  • 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
  • ...\&\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
  • 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
  • ...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
  • ...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
  • ...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
  • <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
  • ...& \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
  • ...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
  • 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
  • [b,s] = size(rates); % banks/sites temp = reshape(temp,b,s)';
    24 KB (2,900 words) - 19:00, 17 January 2012
  • ...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
  • ==Appendix B - The Matlab Interface Routines - Utility Routines== *[[Xpress Appendix B|Appendix B]]
    3 KB (441 words) - 06:59, 28 September 2011
  • |''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
  • ...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
  • B = [1;0]; nu = size(B,2); % Number of inputs
    4 KB (591 words) - 09:33, 8 November 2011
  • 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
  • ==Appendix B - The Matlab Interface Routines - Test Routines== *[[GUROBI Appendix B|Appendix B]]
    2 KB (261 words) - 04:11, 4 October 2011
  • > 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
  • ...= ''&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
  • ==Appendix B: The Matlab Interface Routines - Utility Routines== * [[CPLEX Appendix B|Appendix B]]
    3 KB (476 words) - 08:52, 13 August 2011
  • ...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
  • 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
  • % Lower and upper bounds on x, expressed as A*x <= b b = [ones(N,1); zeros(N,1)];
    4 KB (420 words) - 08:07, 23 September 2014
  • Prob.user.b = b; If for example the objective function needs the additional variables a and b do the following in the file:
    10 KB (1,435 words) - 18:41, 17 January 2012
  • |||''QP.B''||Active set ''B 0 ''at start: ''B''(''i'') = 1: Include variable ''x''(''i'') is in basic set.
    3 KB (464 words) - 08:13, 16 January 2012
  • |||''bTol''||Accuracy for satisfying ''Ax ''+ ''D''<sub>2</sub>''r ''= ''b'', ''A<sup>T</sup> y ''+ ''z ''= ''&nabla;f ''(''x'') and ''x - x''1 = ''b {} & & & Ax & = & b \\
    6 KB (844 words) - 10:55, 6 August 2014
  • ...ent to Func set them in Prob as a structure. Example for parameters a and b: Prob.user.a = a; Prob.user.b = b;
    1 KB (190 words) - 08:07, 10 January 2012
  • ...<sup>(''k'')</sup>), ''f''(b<sup>(''k'')</sup> ) and ''f<nowiki>'</nowiki>(b''<sup>(''k'')</sup>) if it is known. The sectioning phase terminates when '
    4 KB (626 words) - 10:57, 8 December 2011
  • Dantzig, G B, Chapter 3.3. In Linear Programming and Extensions. Princeton University Pr b = [325;300;275];
    2 KB (222 words) - 09:35, 8 November 2011
  • <math> \frac{dx}{dt} = A*x + B*u </math> B = [0 0; 1/m1 0;
    3 KB (351 words) - 05:28, 14 February 2012
  • ...endix_B#Table:_The_state_variable_xState_for_the_variable.|TOMLAB Appendix B]]. ...ble:_The_state_variable_bState_for_each_linear_constraint.|TOMLAB Appendix B]].
    15 KB (2,234 words) - 10:25, 9 March 2015
  • ...endix_B#Table:_The_state_variable_xState_for_the_variable.|TOMLAB Appendix B]]. ...ble:_The_state_variable_bState_for_each_linear_constraint.|TOMLAB Appendix B]].
    17 KB (2,524 words) - 10:34, 9 March 2015
  • ...se subfields of ''Prob.user''. It the user wants to send some variables a, B and C, then, after creating the ''Prob'' structure, these extra variables a Prob.user.B=B;
    17 KB (2,613 words) - 10:20, 5 August 2014
  • |||''b_L''||Lower bounds on the linear constraints. ''b |||''xState''||State of each variable, described in [[TOMLAB Appendix B]].
    7 KB (1,058 words) - 08:08, 10 January 2012
  • ...endix_B#Table:_The_state_variable_xState_for_the_variable.|TOMLAB Appendix B]]. ...ble:_The_state_variable_bState_for_each_linear_constraint.|TOMLAB Appendix B]].
    10 KB (1,539 words) - 11:24, 19 August 2013
  • &gt;&gt; toms a b % Create two symbolic objects &gt;&gt; a + b % Add them together
    3 KB (464 words) - 05:58, 15 December 2015
  • ...ced out by a point acted on only by gravity, which starts at A and reaches B in the shortest time." In this example, we solve the problem numerically for A = (0,0) and B = (10,-3), and an initial speed of zero.
    3 KB (396 words) - 04:52, 14 February 2012
  • a = 1; b = 3; x0 = icollocate(x == 2*abs(b-a)*t.*(t-2*(0.25+(b<a)*0.5))+1);
    2 KB (242 words) - 05:05, 14 February 2012
  • b = 1.4; a*z(:,4) <= k <= b*z(:,4)
    4 KB (226 words) - 09:34, 8 November 2011
  • ''(b) '''''if '''<math>\|d^{(k)}\|_{\infty} < \rho^k</math> '''then ''' ...Step ''(d) ''above) or until a feasible QP problem is encountered (Step ''(b) ''above). This heuristic is motivated by the success of nonlinear branch-
    37 KB (5,823 words) - 16:47, 19 January 2012
  • b = length(values); % Bonds to buy buy = tom('buy',b,1,'int');
    6 KB (718 words) - 09:33, 8 November 2011
  • ...traints. For equality constraints (or fixed variables), set e.g. b L(k) == b U(k).
    27 KB (4,279 words) - 11:21, 17 December 2011
  • ...tion is only possible if a flow from Nice to Nantes is established so that B may answer A. In digital telephone networks, the binary flows all have the
    8 KB (967 words) - 09:34, 8 November 2011
  • ...traints. For equality constraints (or fixed variables), set e.g. b L(k) == b U(k). |''QP.B''||Basis vector in TOMLAB QP standard.
    12 KB (1,770 words) - 04:56, 23 June 2015
  • ...ic Algorithm Energy Minimization for Point Charges on a Sphere. Phys. Rev. B. 53 (1996), R1740-R1743. Saff, E B, and Kuijlaars, A, Distributing Many Points on the Sphere. Math. Intelligen
    4 KB (467 words) - 09:34, 8 November 2011
  • & \text{subject to}& A x = b, &x \ge 0, b^T = (1, 0,...,0) \in R^{ m+1 }.
    22 KB (2,948 words) - 06:31, 29 November 2012
  • b = length(weights); load = tom('load',b,w,'int');
    4 KB (454 words) - 09:35, 8 November 2011
  • J = a * [ t.*e1+(e2-e1)*(1-1/b), -t.*e2+(e2-e1)/b, (e1-e2)/x(3) ];
    24 KB (3,672 words) - 14:09, 14 January 2012
  • A + B -> X where x1 = [A][B], x2 = [X] and x3 = [Y]. The initial condition is
    5 KB (664 words) - 04:57, 14 February 2012
  • b = [b; 100000-c; -50000+c];
    10 KB (1,465 words) - 08:34, 21 January 2015
  • \min\limits_{x} & f(x)= \frac{1}{2}\sum\limits_1^6 r_i(x)^2 \\s/t & Ax \geq b \\ & x \geq 0 \\ b = \left(
    19 KB (2,996 words) - 08:34, 10 January 2012
  • b = 500; D = 0.5*620*v.^2.*exp(-b*h);
    5 KB (575 words) - 05:03, 14 February 2012
  • |||''xState''||State of each variable, described in [[TOMLAB Appendix B]]. ...'bState''||State of each linear constraint, described in [[TOMLAB Appendix B]].
    7 KB (968 words) - 08:09, 10 January 2012
  • plot(t,vr,'r*-',t,vt,'b*-'); plot(t,ur,'r+-',t,ut,'b+-');
    5 KB (578 words) - 05:35, 14 February 2012
  • ...nt value", e.g. if the constraint is Ax ''<''= b, the weight is EqCon- Fac/b If DIRECT just is pushing down the f(x) value instead of fulfilling the e
    13 KB (1,975 words) - 08:10, 16 January 2012
  • ...of Batch Processes II. Role of Measurements in Handling Uncertainty 2001, B. Srinivasan, D. Bonvin, E. Visser, S. Palanki This particular example was featured in the work of B. Srinivasan et al. 2001. The optimal trajectories for the problem was provi
    8 KB (989 words) - 05:32, 14 February 2012
  • ...nt value", e.g. if the constraint is Ax ''<''= b, the weight is EqCon- Fac/b If DIRECT just is pushing down the f(x) value instead of fulfilling the e
    13 KB (2,009 words) - 08:11, 16 January 2012
  • E. B. LIM(1), Y. Q. LIU(2), K. L. TEO(2) AND J. B. MOORE(1)
    3 KB (409 words) - 05:31, 14 February 2012
  • [m,b] = size(batches); temp = reshape(Result.x_k,m,b);
    28 KB (3,023 words) - 18:57, 17 January 2012
  • Dantzig, G B, Chapter 3.4. In Linear Programming and Extensions. Princeton University Pr alloy: products on the market (a, b, c, d, e, f, g, h, i)
    2 KB (206 words) - 09:32, 8 November 2011
  • % explanation. Suppose that a person A at Nantes calls a person B at % a flow from Nice to Nantes is established so that B may answer A.
    27 KB (3,266 words) - 19:00, 17 January 2012
  • b = size(rates,1); borrow = tom('borrow',b,s);
    3 KB (421 words) - 09:33, 8 November 2011
  • ''b U'' Upper bounds on the linear constraints.
    3 KB (389 words) - 08:16, 10 January 2012
  • v: vendors (a, b, c, d, e)
    3 KB (351 words) - 09:32, 8 November 2011
  • \mathbb{R}^{m_2}</math>, <math>L \in \mathbb{R}^{n \times b}</math> and <math>\alpha \in \mathbb{R}^{1}</math>.
    2 KB (320 words) - 18:12, 17 January 2012
  • Three jobs (A,B,C) must be executed sequentially in three steps, but not all jobs require a
    2 KB (254 words) - 09:33, 8 November 2011
  • |[[CPLEX Appendix B#abc2gap|abc2gap]]||Utility to convert a Generalized Assignment Problem (GAP
    2 KB (253 words) - 14:41, 18 January 2012
  • for i=1:n1 %b
    4 KB (526 words) - 09:33, 8 November 2011
  • |''QP.B''||Basis vector in TOMLAB QP standard. |1.||PRINT LEVEL||0||0||11111||JFLXB: Jac, fCon, lambda, x, B=LU stats
    21 KB (3,165 words) - 14:10, 22 January 2012
  • |[[Xpress Appendix B#abc2gap|abc2gap]]||Utility to convert a Generalized Assignment Problem (GAP
    2 KB (282 words) - 13:25, 22 January 2012
  • |''LCBB''||Lower Confidence Bounding parameter b<br>Default 2
    16 KB (2,435 words) - 17:19, 21 June 2014
  • |''B''||Logical vector of the same length as the number of variables. A zero cor |''tau2''||How near end point of [''a, b''] (0''.''1).
    31 KB (4,594 words) - 07:56, 16 January 2012
  • Batch reactor with reactions: A -> B -> C.
    3 KB (354 words) - 04:42, 14 February 2012
  • |''Result''||Result structure, see [[TOMLAB Appendix B]].
    7 KB (1,032 words) - 08:28, 16 January 2012
  • The boundary conditions are still A = (0,0), B = (10,-3), and an initial speed of zero, so we have
    3 KB (371 words) - 04:53, 14 February 2012
  • |''LS''||Statistical information about the solution. See [[TOMLAB Appendix B]].
    3 KB (323 words) - 08:10, 10 January 2012
  • A robot with obstacles in 2D space. Travel from point A to B using minimum energy.
    6 KB (638 words) - 05:34, 14 February 2012
  • |||''xState''||State of each variable, described in [[TOMLAB Appendix B]].
    3 KB (463 words) - 08:17, 16 January 2012
  • Batch reactor with reactions: A -> B and A -> C.
    3 KB (308 words) - 05:32, 14 February 2012
  • |||''xState''||State of each variable, described in [[TOMLAB Appendix B]].
    5 KB (657 words) - 08:08, 10 January 2012
  • [m,b] = size(batches);
    5 KB (547 words) - 09:32, 8 November 2011