nonlinear inequality constraint for fmincon()

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Susan 2019-4-23

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编辑： Susan 2019-5-22

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Hey guys,

I am trying to write down the below nonlinear inequality constraint

Calculate_W_S_R(J, I, K, tr_prob, Tp, Tavg, Pf, Wrate) <= rateTh

in the form of c(x)<=0. However, when I want to define the constraint function, i.e., function[c ceq] = constraint(x), the input get more parameters than only the single variable x. Any idea how can I deal with this issue? Thanks in advance

the nonlinear inequality constraint c is a function of variable ptilda (the optimization variable which shows up in "Wrate") and some other given parameter (J, I, K, tr_prob, Tp, Tavg, Pf, ateTh). Wrate is a function of J, I, K, TB, ps, UE_A, SINR where SINR is a function of ptilda.

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Walter Roberson 2019-4-23

The nonlcon slot in fmincon() calls needs to receive a function handle to a function that accepts a single variable. It is not technically mandatory to pass that variable into the function to be invoked. However, if you do not pass that variable into the function, then you are dealing with one of the following situations:

The function always returns the same value. If this is the case, it is ineffective as a constraint: just evaluate the result of the function once, and if the constraint is violated then do not bother doing the minimization becaus it would not be possibe for the constraint to not be violated at any location when the function is constant
The function uses randomness. The return value would not always violate the constraint, so minimization could proceed. However, fmincon()'s algorithms are only defined for continuous functions, and any randomness makes the functions discontinuous
The function uses shared or global variables and values stored during calls to other functions to make the decision. This is not a good design, and it will also fail subtly. fmincon() is permitted to make the nonlcon calls in any order relative to calls to the objective function, and when it is trying to find values that satisfy nonlinear equality constraints it will call the nonlcon multiple times without having called the objective function. Do not design your optimization this way: instead define a function to calculate the value from the inputs and call the function from both locations. It is valid to put a cache on a function such as that, perhaps using memoize(), to avoid re-computing if the parameters happen to be the same.

Walter Roberson 2019-5-9

The tools in the global optimization toolbox help you try to solve all kinds of optimizations. They never make any promises that they will definitely solve it, but they are not restricted to searching local minima.

ga() and gamultiobj() in particular do not require that the objective be continuous to any level of derivative, and can deal with discrete problems or mixed integer.

The algorithms used by fmincon() (base MATLAB, no toolbox needed) work best with convex optimizations, but you can add non-linear constraints that have the effect of making the search area non-convex. However, it cannot handle discrete or mixed integer problems at all, and the function is required to be continuous within the regions that are not prohibitted.

Susan 2019-5-10