There are four general categories of Optimization Toolbox™ solvers:
This group of solvers attempts to find a local minimum of the objective
function near a starting point
x0. They address problems
of unconstrained optimization, linear programming, quadratic programming,
and general nonlinear programming.
This group of solvers attempts to either minimize the maximum value of a
set of functions (
fminimax), or to find a location
where a collection of functions is below some prespecified values
This group of solvers attempts to find a solution to a scalar- or
vector-valued nonlinear equation f(x) = 0 near a starting point
Equation-solving can be considered a form of optimization because it is
equivalent to finding the minimum norm of f(x) near
This group of solvers attempts to minimize a sum of squares. This type of problem frequently arises in fitting a model to data. The solvers address problems of finding nonnegative solutions, bounded or linearly constrained solutions, and fitting parametrized nonlinear models to data.
For more information see Problems Handled by Optimization Toolbox Functions. See Optimization Decision Table for aid in choosing among solvers for minimization.
Minimizers formulate optimization problems in the form
possibly subject to constraints. f(x) is called an objective function. In general, f(x) is a scalar function of type
x is a vector or scalar of type
However, multiobjective optimization, equation solving, and some sum-of-squares
minimizers, can have vector or matrix objective functions F(x) of type
double. To use Optimization
Toolbox solvers for maximization instead of minimization, see Maximizing an Objective.
Write the objective function for a solver in the form of a function file or anonymous function handle. You can supply a gradient ∇f(x) for many solvers, and you can supply a Hessian for several solvers. See Write Objective Function. Constraints have a special form, as described in Write Constraints.