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Find minimum of semi-infinitely constrained multivariable nonlinear function

`fseminf`

is a nonlinear programming solver that finds the
minimum of a problem specified by

$$\underset{x}{\mathrm{min}}f(x)\text{suchthat}\{\begin{array}{c}A\cdot x\le b,\\ Aeq\cdot x=beq,\\ lb\le x\le ub,\\ c(x)\le 0,\\ ceq(x)=0,\\ {K}_{i}(x,{w}_{i})\le 0,\text{}1\le i\le n.\end{array}$$

*b*and*beq*are vectors.*A*and*Aeq*are matrices.*c*(*x*),*ceq*(*x*), and*K*(_{i}*x,w*) are functions that return vectors._{i}*f*(*x*) is a function that returns a scalar.

*f*(*x*), *c*(*x*), and
*ceq*(*x*) can be nonlinear functions. The vectors (or
matrices) *K _{i}*(

*x*, *lb*, and *ub* can be passed as
vectors or matrices; see Matrix Arguments.

The function to be minimized, the constraints, and the semi-infinite constraints must be continuous functions of

`x`

and`w`

.`fseminf`

might give local solutions only.

`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.