Solve mixed integer quadtratic programming problems.
Solve mixed integer quadtratic programming problems.
x = cplexmiqp(H,f,Aineq,bineq) x = cplexmiqp(H,f,Aineq,bineq,Aeq,beq) x = cplexmiqp(H,f,Aineq,bineq,Aeq,beq,sostype,sosind,soswt) x = cplexmiqp(H,f,Aineq,bineq,Aeq,beq,sostype,sosind,soswt,lb,ub) x = cplexmiqp(H,f,Aineq,bineq,Aeq,beq,sostype,sosind,soswt,lb,ub,ctype) x = cplexmiqp(H,f,Aineq,bineq,Aeq,beq,sostype,sosind,soswt,lb,ub,ctype,x0) x = cplexmiqp(H,f,Aineq,bineq,Aeq,beq,sostype,sosind,soswt,lb,ub,ctype,x0,options) x = cplexmiqp(problem) [x,fval] = cplexmiqp(...) [x,fval,exitflag] = cplexmiqp(...) [x,fval,exitflag,output] = cplexmiqp(...)
Finds the minimum of a problem specified by
min 0.5*x'*H*x+f*x or f*x st. Aineq*x <= bineq Aeq*x = beq lb <= x <= ub
x is a BICSN vector -- that is, its individual entries are each required to be binary, general integer, continuous, semi-continuous or semi-integer.
H | Symmetric double matrix for objective function | |
f | Double column vector for linear objective function | |
Aineq | Double matrix for linear inequality constraints | |
bineq | Double column vector for linear inequality constraints | |
Aeq | Double matrix for linear equality constraints | |
beq | Double column vector for linear equality constraints | |
sostype | String with possible char values '1', '2' | |
sosind | Double column vector or column vector cell of indices for the SOSs to be added | |
soswt | Double column vector or column vector cell of weights for the SOSs to be added | |
lb | Double column vector of lower bounds | |
ub | Double column vector of upper bounds | |
ctype | String with possible char values 'B','I','C','S','N'; set ctype(j) to 'B', 'I','C', 'S', or 'N' to indicate that x(j) should be binary, general integer, continuous, semi-continuous or semi-integer (respectively). | |
x0 | Double column vector of initial point of x | |
options | Options structure created with cplexoptimset | |
problem | Structure containing the following fields: H: Symmetric double matrix for objective function f: Double column vector for linear objective function Aineq: Double matrix for linear inequality constraints bineq: Double column vector for linear inequality constraints Aeq: Double matrix for linear equality constraints beq: Double column vector for linear equality constraints sos: Struct vector representing the SOSs sos(i).type: String with possible char values '1', '2' sos(i).ind: Double column vector of indices for the SOSs to be added sos(i).wt: Double column vector of weights for the SOSs to be added lb: Double column vector of lower bounds ub: Double column vector of upper bounds ctype: String with possible char values 'B','I','C','S','N'; set ctype(j) to 'B', 'I','C', 'S', or 'N' to indicate that x(j) should be binary, general integer, continuous, semi-continuous or semi-integer (respectively) x0: Double column vector for initial point of x options: Options structure created with cplexoptimset |
x | Solution found by the optimization function. If exitflag > 0, then x is a solution; otherwise, x is the value of the optimization routine when it terminated prematurely. | |
fval | Value of the objective function at the solution x | |
exitflag | Integer identifying the reason the optimization algorithm terminated | |
output | Structure containing information about the optimization. The fields of the structure are: iterations: Number of iterations algorithm: Optimization algorithm used message: Exit message time: Execution time of the algorithm cplexstatus: Status code of the solution cplexstatusstring: Status string of the solution |
x = cplexmiqp(H, f, Aineq, bineq) solves the mixed integer quadratic programming problem min 1/2*x'*H*x + f*x subject to Aineq*x <= bineq. If no quadratic objective term exists, set H=[].x = cplexmiqp(H, f, Aineq, bineq, Aeq, beq) solves the preceding problem with the additional equality constraints Aeq*x = beq. If no inequalities exist, set Aineq=[] and bineq=[].
x = cplexmiqp(H, f, Aineq, bineq, Aeq, beq, sostype, sosind, soswt) solves the preceding problem with the additional requirement that the SOS constraints are satisfied. If no equalities exist, set Aeq=[] and beq=[].
x = cplexmiqp(H, f, Aineq, bineq, Aeq, beq, sostype, sosind, soswt, lb, ub) defines a set of lower and upper bounds on the design variables, x, so that the solution is always in the range lb <= x <= ub. If no SOS constraints exist, set sostype=[], sosind=[] and soswt=[].
x = cplexmiqp(H, f, Aineq, bineq, Aeq, beq, sostype, sosind, soswt, lb, ub, ctype) defines the types for each of the design variables. If no bounds exist, set lb=[] and ub=[].
x = cplexmiqp(H, f, Aineq, bineq, Aeq, beq, sostype, sosind, soswt, lb, ub, ctype, x0) sets the starting point for the algorithm to x0. If all design variables are continuous, set ctype=[].
x = cplexmiqp(H, f, Aineq, bineq, Aeq, beq, sostype, sosind, soswt, lb, ub, ctype, x0, options) minimizes with the default optimization options replaced by values in the structure options, which can be created using the function cplexoptimset. If you do not want to give an initial point, set x0=[].
x = cplexmiqp(problem) where problem is a structure.
[x,fval] = cplexmiqp(...) returns the value of the objective function at the solution x: fval = 0.5*x'*H*x + f*x.
[x,fval,exitflag] = cplexmiqp(...) returns a value exitflag that describes the exit condition of cplexmiqp.
[x,fval,exitflag,output] = cplexmiqp(...) returns a structure output that contains information about the optimization.
NOTE: If there are no lower bounds specified (that is, either [] passed in for lb or a form of the function without lb is used), then -Inf will be used as lower bound for all variables.
See cplexmiqcp for a description of exitflag values.
See also cplexoptimset.