Problem-Based Optimization Algorithms
solve can call a
solver, the problems must be converted to solver form, either by
some other associated functions or objects. This conversion entails, for example, linear
constraints having a matrix representation rather than an optimization variable
The first step in the algorithm occurs as you place
optimization expressions into the problem. An
OptimizationProblem object has an internal list of the variables used in its
expressions. Each variable has a linear index in the expression, and a size. Therefore, the
problem variables have an implied matrix form. The
function performs the conversion from problem form to solver form. For an example, see Convert Problem to Structure.
For nonlinear optimization problems,
solve uses automatic
differentiation to compute the gradients of the objective function and
nonlinear constraint functions. These derivatives apply when the objective and constraint
functions are composed of Supported Operations for Optimization Variables and Expressions and do not use the
function. When automatic differentiation does not apply, solvers estimate derivatives using
finite differences. For details of automatic differentiation, see Automatic Differentiation Background.
For the default and allowed solvers that
solve calls, depending on the problem objective and constraints, see
'solver'. You can override the default by using the
'solver' name-value pair argument when calling
For the algorithm that
intlinprog uses to solve MILP problems, see intlinprog Algorithm. For
the algorithms that
linprog uses to solve linear programming problems,
see Linear Programming Algorithms.
For the algorithms that
quadprog uses to solve quadratic programming
problems, see Quadratic Programming Algorithms. For linear or nonlinear least-squares solver
algorithms, see Least-Squares (Model Fitting) Algorithms. For nonlinear solver algorithms, see Unconstrained Nonlinear Optimization Algorithms and
Constrained Nonlinear Optimization Algorithms.
For nonlinear equation solving,
solve internally represents each
equation as the difference between the left and right sides. Then
attempts to minimize the sum of squares of the equation components. For the algorithms for
solving nonlinear systems of equations, see Equation Solving Algorithms. When
the problem also has bounds,
to minimize the sum of squares of equation components. See Least-Squares (Model Fitting) Algorithms.
If your objective function is a sum of squares, and you want
to recognize it as such, write it as either
sum(expr.^2), and not as
expr'*expr or any
other form. The internal parser recognizes a sum of squares only when represented as a
square of a norm or an explicit sums of squares. For details, see Write Objective Function for Problem-Based Least Squares. For an example, see
Nonnegative Linear Least Squares, Problem-Based.