Writing Objective Functions for Linear or Quadratic Problems

The following solvers handle linear or quadratic objective functions:

• linprog and intlinprog: minimize

  f'x = f(1)*x(1) + f(2)*x(2) +...+ f(n)*x(n).

  Input the vector f for the objective. See the examples in Linear Programming and Mixed-Integer Linear Programming.

• lsqlin and lsqnonneg: minimize

  ‖Cx - d‖.

  Input the matrix C and the vector d for the objective. See Nonnegative Linear Least Squares, Solver-Based.

• quadprog: minimize

  1/2 * x'Hx + f'x
  = 1/2 * (x(1)*H(1,1)*x(1) + 2*x(1)*H(1,2)*x(2) +...
+ x(n)*H(n,n)*x(n)) + f(1)*x(1) + f(2)*x(2) +...+ f(n)*x(n).

  Input both the vector f and the symmetric matrix H for the objective. See Quadratic Programming and Cone Programming.