fseminf
Find minimum of semi-infinitely constrained multivariable nonlinear function
Syntax
Description
fseminf
is a nonlinear programming solver that finds the
minimum of a problem specified by
b and beq are vectors.
A and Aeq are matrices.
c(x), ceq(x), and Ki(x,wi) are functions that return vectors.
f(x) is a function that returns a scalar.
f(x), c(x), and ceq(x) can be nonlinear functions. The vectors (or matrices) Ki(x,wi) ≤ 0 are continuous functions of both x and an additional set of variables w1,w2,...,wn. The variables w1,w2,...,wn are vectors of length two, at most.
x, lb, and ub can be passed as vectors or matrices; see Matrix Arguments.
Examples
Input Arguments
Output Arguments
Limitations
The function to be minimized, the constraints, and the semi-infinite constraints must be continuous functions of
x
andw
.fseminf
might give local solutions only.
Algorithms
fseminf
uses cubic and quadratic interpolation techniques to estimate
peak values in the semi-infinite constraints. The algorithm uses the peak values to form a set
of constraints supplied to an SQP method, as in the fmincon
function. When the number of constraints changes, the algorithm
reallocates Lagrange multipliers to the new set of constraints.
The recommended sampling interval calculation uses the difference between the interpolated peak values and the peak values in the data set to estimate whether the function needs to take more or fewer points. The function also evaluates the effectiveness of the interpolation by extrapolating the curve and comparing it to other points in the curve. The recommended sampling interval decreases when the peak values are close to constraint boundaries, that is, zero.
When the problem is not feasible, fseminf
attempts to minimize the
maximum constraint value.
For more details on the algorithm used and the types of procedures displayed under the
Procedures
heading when the Display
option is set to
'iter'
with optimoptions
, see SQP Implementation. For more details on the fseminf
algorithm,
see fseminf Problem Formulation and Algorithm.