


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.
USE SYMBOLIC MATH TOOLBOX MATLAB CODE
MatlabFunction generates code that depends on the orientation of input vectors. See Use Assumptions on Symbolic Variables.

When modeling your problem, use assumptions to return the right results.
USE SYMBOLIC MATH TOOLBOX MATLAB SERIES
It is much more efficient to use matlabFunction. Using Symbolic Math Toolbox, you can differentiate and integrate symbolic expressions, perform series expansions, find transforms of symbolic expressions, and perform vector calculus operations by using the listed functions. 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. Your computations can be performed either analytically or using variable-precision arithmetic, with the results displayed in mathematical typeset. You can perform dimensional computations and convert between units. Optimization objective and constraint functions should be defined in terms of a vector, say x. Symbolic Math Toolbox lets you analytically perform differentiation, integration, simplification, transforms, and equation solving.
