lsqlin Solves a linear quadratic problem. x = lsqlin(C,d,A,b) x = lsqlin(C,d,A,b,Aeq,beq) x = lsqlin(C,d,A,b,Aeq,beq,lb,ub) x = lsqlin(C,d,A,b,Aeq,beq,lb,ub,x0) x = lsqlin(C,d,A,b,Aeq,beq,lb,ub,x0,param) [xopt,resnorm,residual,exitflag,output,lambda] = lsqlin( ... ) C : a matrix of doubles, represents the multiplier of the solution x in the expression C*x - d. C is M-by-N, where M is the number of equations, and N is the number of elements of x. d : a vector of doubles, represents the additive constant term in the expression C*x - d. d is M-by-1, where M is the number of equations. A : a vector of doubles, represents the linear coefficients in the inequality constraints b : a vector of doubles, represents the linear coefficients in the inequality constraints Aeq : a matrix of doubles, represents the linear coefficients in the equality constraints beq : a vector of doubles, represents the linear coefficients in the equality constraints LB : a vector of doubles, contains lower bounds of the variables. UB : a vector of doubles, contains upper bounds of the variables. x0 : a vector of doubles, contains initial guess of variables. param : a list containing the the parameters to be set. xopt : a vector of doubles, 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 doubles, solution residuals returned as the vector C*x-d. exitflag : Integer identifying the reason the algorithm terminated. output : Structure containing information about the optimization. lambda : Structure containing the Lagrange multipliers at the solution x (separated by constraint type). 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 \leq beq \\ & & lb \leq x \leq ub \\ \end{eqnarray} We are calling IPOpt for solving the linear least square problem, IPOpt is a library written in C++. The code has been written by ​Andreas Wächter and ​Carl Laird. Harpreet Singh