Now we calculate the Hessians of the two constraint functions, and make function handle versions with matlabFunction.Once the robot’s joint angles are calculated using the inverse kinematics, a motion profile can be generated using the Jacobian matrix to move the end-effector from the initial to the target pose. We calculated the Hessian of the objective function in the first example. For the current constraint, there are no linear equalities, so we use the two multipliers lambda.ineqnonlin(1) and lambda.ineqnonlin(2). The parts of the lambda structure that you use for nonlinear constraints are lambda.ineqnonlin and lambda.eqnonlin. The Hessian function takes two input arguments: the position vector x, and the Lagrange multiplier structure lambda. Its Hessian is the Hessian of the Lagrangian see the User's Guide for more information. This is because a nonlinearly constrained function needs to include those constraints in its Hessian. The interior-point algorithm requires its Hessian function to be written as a separate function, instead of being part of the objective function. Gradc = jacobian(c,x).' % transpose to put in correct formĬonstraint = matlabFunction(c,gradc, 'vars',) Since fmincon calls the objective function with column vectors, you must be careful to call matlabFunction with column vectors of symbolic variables. MatlabFunction generates code that depends on the orientation of input vectors.

It is much more efficient to use matlabFunction.

Therefore you should perform this calculation only once, and generate code, via matlabFunction, to call during execution of the solver.Įvaluating symbolic expressions with the subs function is time-consuming. This means that a symbolic gradient or Hessian has to be placed in the appropriate place in the objective or constraint function file or function handle.Ĭalculating gradients and Hessians symbolically can be time-consuming.

Optimization gradients, and sometimes Hessians, are supposed to be calculated within the body of the objective or constraint functions. This requires you to translate between vectors and scalars. However, symbolic variables are scalar or complex-valued, not vector-valued. Optimization objective and constraint functions should be defined in terms of a vector, say x.

Symbolic math toolbox function block