lsqlin Solves a linear quadratic problem. xopt = lsqlin(C,d,A,b) xopt = lsqlin(C,d,A,b,Aeq,beq) xopt = lsqlin(C,d,A,b,Aeq,beq,lb,ub) xopt = lsqlin(C,d,A,b,Aeq,beq,lb,ub,x0) xopt = lsqlin(C,d,A,b,Aeq,beq,lb,ub,x0,param) [xopt,resnorm,residual,exitflag,output,lambda] = lsqlin( ... ) 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 d-C*x. exitflag : A flag showing returned exit flag from Ipopt. 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 constraint multiplier. Search the minimum of a constrained linear least square problem specified by : \begin{eqnarray} &\mbox{min}_{x} & 1/2||C⋅x - d||_2^2 \\ & \text{subject to} & A⋅x \leq b \\ & & Aeq⋅x = beq \\ & & lb \leq x \leq ub \\ \end{eqnarray} The routine calls Ipopt for solving the linear least square problem, Ipopt is a library written in C++. Harpreet Singh