Optimization Toolbox™ solvers accept vectors for many arguments, such as the initial point
x0, lower bounds
lb, and upper bounds
ub. They also accept matrices for these arguments, where matrix
means an array of any size. When your solver arguments are naturally arrays, not
vectors, feel free to provide the arguments as arrays.
Here is how solvers handle matrix arguments.
Internally, solvers convert matrix arguments into vectors before processing. For example,
x0(:). For an explanation of this syntax, see the
colon, or the "Indexing with a Single Index" section of Array Indexing.
For output, solvers reshape the solution
xto the same size as the input
x0is a matrix, solvers pass
xas a matrix of the same size as
x0to both the objective function and to any nonlinear constraint function.
Linear Constraints, though, take
xin vector form,
x(:). In other words, a linear constraint of the form
A*x ≤ bor
Aeq*x = beq
xas a vector, not a matrix. Ensure that your matrix
Aeqhas the same number of columns as
x0has elements, or the solver will error.