linprog

Parameters

c : +: a vector of double, contains coefficients of the variables in the objective
A : +: a matrix of double, represents the linear coefficients in the inequality constraints A⋅x ≤ b.
b : +: a vector of double, represents the linear coefficients in the inequality constraints A⋅x ≤ b.
Aeq : +: a matrix of double, represents the linear coefficients in the equality constraints Aeq⋅x = beq.
beq : +: a vector of double, represents the linear coefficients in the equality constraints Aeq⋅x = beq.
lb : +: Lower bounds, specified as a vector or array of double. lb represents the lower bounds elementwise in lb ≤ x ≤ ub.
ub : +: Upper bounds, specified as a vector or array of double. ub represents the upper bounds elementwise in lb ≤ x ≤ ub.
options : +: a list containing the parameters to be set.
file : +: a string describing the path to the mps file.
xopt : +: a vector of double, the computed solution of the optimization problem.
fopt : +: a double, the value of the function at x.
status : +: status flag returned from symphony. See below for details.
output : +: The output data structure contains detailed information about the optimization process. See below for details.
lambda : +: The structure consist of the Lagrange multipliers at the solution of problem. See below for details.

Description

OSI-CLP is used for solving the linear programming problems, OSI-CLP is a library written in C++. +Search the minimum of a constrained linear programming problem specified by :

The routine calls Clp for solving the linear programming problem, Clp is a library written in C++.

The options allows the user to set various parameters of the Optimization problem. +It should be defined as type "list" and contains the following fields. In the current version it only contains maxiter. +

Syntax : options= list("MaxIter", [---]);
MaxIter : a Scalar, containing the Maximum Number of Iteration that the solver should take.
Default Values : options = list("MaxIter", [3000]);

The exitflag allows to know the status of the optimization which is given back by CLP. +

exitflag=0 : Optimal Solution Found
exitflag=1 : Primal Infeasible
exitflag=2 : Dual Infeasible
exitflag=3 : Maximum Number of Iterations Exceeded. Output may not be optimal.
exitflag=4 : Solution Abandoned
exitflag=5 : Primal objective limit reached.
exitflag=6 : Dual objective limit reached.

The output data structure contains detailed informations about the optimization process. +It has type "struct" and contains the following fields. +

output.iterations: The number of iterations performed during the search
output.constrviolation: The max-norm of the constraint violation.

The lambda data structure contains the Lagrange multipliers at the end +of optimization. In the current version the values are returned only when the the solution is optimal. +It has type "struct" and contains the following fields. +

lambda.lower: The Lagrange multipliers for variable lower bounds.
lambda.eqlin: The Lagrange multipliers for the linear equality constraints.
lambda.ineqlin: The Lagrange multipliers for the linear inequality constraints.

Examples

//Optimal problems
+//Linear program, linear inequality constraints
+c=[-1,-1/3]'
+A=[1,1;1,1/4;1,-1;-1/4,-1;-1,-1;-1,1]
+b=[2,1,2,1,-1,2]
+[xopt,fopt,exitflag,output,lambda]=linprog(c, A, b)
+// Press ENTER to continue

Examples

//Linear program with Linear Inequalities and Equalities`
+c=[-1,-1/3]'
+A=[1,1;1,1/4;1,-1;-1/4,-1;-1,-1;-1,1]
+b=[2,1,2,1,-1,2]
+Aeq=[1,1/4]
+beq=[1/2]
+[xopt,fopt,exitflag,output,lambda]=linprog(c, A, b, Aeq, beq)
+// Press ENTER to continue

Examples

//Linear program with all constraint types
+c=[-1,-1/3]'
+A=[1,1;1,1/4;1,-1;-1/4,-1;-1,-1;-1,1]
+b=[2,1,2,1,-1,2]
+Aeq=[1,1/4]
+beq=[1/2]
+lb=[-1,-0.5]
+ub=[1.5,1.25]
+[xopt,fopt,exitflag,output,lambda]=linprog(c, A, b, Aeq, beq, lb, ub)
+// Press ENTER to continue

Examples

//Primal Infeasible Problem
+c=[-1,-1,-1]'
+A=[1,2,-1]
+b=[-4]
+Aeq=[1,5,3;1,1,0]
+beq=[10,100]
+lb=[0,0,0]
+ub=[%inf,%inf,%inf]
+[xopt,fopt,exitflag,output,lambda]= linprog(c,A,b,Aeq,beq,lb,ub)
+// Press ENTER to continue

Examples

//Dual Infeasible Problem
+c=[3,5,-7]'
+A=[-1,-1,4;1,1,4]
+b=[-8,5]
+Aeq=[]
+beq=[]
+lb=[-%inf,-%inf,-%inf]
+ub=[%inf,%inf,%inf]
+[xopt,fopt,exitflag,output,lambda]= linprog(c,A,b,Aeq,beq,lb,ub)
+// Press ENTER to continue

Examples

filepath = get_absolute_file_path('linprog.dem.sce');
+filepath = filepath + "exmip1.mps"
+[xopt,fopt,exitflag,output,lambda] =linprog(filepath)

Authors

Bhanu Priya Sayal, Guru Pradeep Reddy

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+ << fminunc + +	+ FOSSEE Optimization Toolbox + +	+ lsqlin >> + +

linprog

Calling Sequence

Parameters

Description

Examples

Examples

Examples

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Examples

Authors