Function File: lsqlin (C, d, A, b)

Function File: lsqlin (C, d, A, b, Aeq, beq, lb, ub)

Function File: lsqlin (C, d, A, b, Aeq, beq, lb, ub, x0)

Function File: lsqlin (C, d, A, b, Aeq, beq, lb, ub, x0, options)

Function File: [x, resnorm, residual, exitflag, output, lambda] = lsqlin (…)

Solve the linear least squares program

min 0.5 sumsq(C*x - d)
x

subject to

A*x <= b,
Aeq*x = beq,
lb <= x <= ub.

The initial guess x0 and the constraint arguments (A and b, Aeq and beq, lb and ub) can be set to the empty matrix ([]) if not given. If the initial guess x0 is feasible the algorithm is faster.

options can be set with optimset, currently the only option is MaxIter, the maximum number of iterations (default: 200).

Returned values:

x

Position of minimum.

resnorm

Scalar value of objective as sumsq(C*x - d).

residual

Vector of solution residuals C*x - d.

exitflag

Status of solution:

0

Maximum number of iterations reached.

-2

The problem is infeasible.

-3

The problem is not convex and unbounded.

1

Global solution found.

output

Structure with additional information, currently the only field is iterations, the number of used iterations.

lambda

Structure containing Lagrange multipliers corresponding to the constraints.

This function calls the more general function quadprog internally.

See also: quadprog.

Demonstration 1

  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];
  %% Linear Inequality Constraints
  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];
  %% Linear Equality Constraints
  Aeq = [3 5 7 9];
  beq = 4;
  %% Bound constraints
  lb = -0.1*ones(4,1);
  ub = ones(4,1);
  [x, resnorm, residual, flag, output, lambda] = lsqlin (C, d, A, b, Aeq, beq, lb, ub)

x =

  -0.1000
  -0.1000
   0.1599
   0.4090

resnorm = 0.1695
residual =

   0.035297
   0.087623
  -0.353251
   0.145270
   0.121232

flag = 1
output =

  scalar structure containing the fields:

    iterations = 3

lambda =

  scalar structure containing the fields:

    lower =

       0.0674
       0.2499
            0
            0

    upper =

       0
       0
       0
       0

    eqlin = -0.016539
    ineqlin =

            0
       0.4982
            0

Package: optim