lsqlin

Parameters

C :

a matrix of double, represents the multiplier of the solution x in the expression C*x - d. Number of columns in C is equal to the number of elements in x.

d :

a vector of double, represents the additive constant term in the expression C*x - d. Number of elements in d is equal to the number of rows in C matrix.

A :

a vector of double, represents the linear coefficients in the inequality constraints

b :

a vector of double, represents the linear coefficients in the inequality constraints

Aeq :

a matrix of double, represents the linear coefficients in the equality constraints

beq :

a vector of double, represents the linear coefficients in the equality constraints

lb :

a vector of double, contains lower bounds of the variables.

ub :

a vector of double, contains upper bounds of the variables.

x0 :

a vector of double, contains initial guess of variables.

param :

a list containing the the parameters to be set.

xopt :

a vector of double, the computed solution of the optimization problem.

resnorm :

a double, objective value returned as the scalar value norm(C*x-d)^2.

residual :

a vector of double, solution residuals returned as the vector C*x-d.

exitflag :

Integer identifying the reason the algorithm terminated. It could be 0, 1 or 2 etc. i.e. Optimal, Maximum Number of Iterations Exceeded, CPU time exceeded. Other flags one can see in the lsqlin macro.

output :

Structure containing information about the optimization. This version only contains number of iterations.

lambda :

Structure containing the Lagrange multipliers at the solution x (separated by constraint type).It contains lower, upper bound multiplier and linear equality, inequality constraints.

Description

Search the minimum of a constrained linear least square problem specified by :

The routine calls Ipopt for solving the linear least square problem, Ipopt is a library written in C++.

Examples

//A simple linear least square example C = [0.9501 0.7620 0.6153 0.4057 0.2311 0.4564 0.7919 0.9354 0.6068 0.0185 0.9218 0.9169 0.4859 0.8214 0.7382 0.4102 0.8912 0.4447 0.1762 0.8936]; d = [0.0578 0.3528 0.8131 0.0098 0.1388]; A = [0.2027 0.2721 0.7467 0.4659 0.1987 0.1988 0.4450 0.4186 0.6037 0.0152 0.9318 0.8462]; b = [0.5251 0.2026 0.6721]; [xopt,resnorm,residual,exitflag,output,lambda] = lsqlin(C,d,A,b) // Press ENTER to continue

Examples

//A basic example for equality, inequality constraints and variable bounds C = [0.9501 0.7620 0.6153 0.4057 0.2311 0.4564 0.7919 0.9354 0.6068 0.0185 0.9218 0.9169 0.4859 0.8214 0.7382 0.4102 0.8912 0.4447 0.1762 0.8936]; d = [0.0578 0.3528 0.8131 0.0098 0.1388]; A =[0.2027 0.2721 0.7467 0.4659 0.1987 0.1988 0.4450 0.4186 0.6037 0.0152 0.9318 0.8462]; b =[0.5251 0.2026 0.6721]; Aeq = [3 5 7 9]; beq = 4; lb = -0.1*ones(4,1); ub = 2*ones(4,1); [xopt,resnorm,residual,exitflag,output,lambda] = lsqlin(C,d,A,b,Aeq,beq,lb,ub)

Authors

• Harpreet Singh