# Optimization problem—constraints not valid? [closed]

I have a model optimization problem: maximize rent, ri, through signals, si and sj, given someone's initial social position, SPi and SPj. Signals have a cost of 1, so the constraint is that D[ri, si] == 1 and D[ri, sj] == 1.

I get the error message

NArgMax::bcons: The following constraints are not valid:

....the whole equation for the constraint here...

Constraints should be equalities, inequalities, or domain specifications involving the variables. >>

I guess my questions are:

• Is the problem simply due to my parameters no allowing a solution within the constraint?

• Can I use the defined variables in the NArgMax inside signalFunc? (should they be defined as functions?)

Is NArgMax the right solution here?

α = 1000;
β = 0.03;
γ = 0.02;
m = 4000;
ω = 1;

ti = (α SPj (β sj - γ ((sj - si)/(sj + sj))^2 + 1)) +
(α SPi (β si - γ ((si - sj)/(si + sj))^2 + 1));
ri = ω (-(tr^2) + 2 m tr) /. tr -> ti

dsi = FullSimplify[D[ri, si],
Assumptions -> {Element[{si, sj}, Reals]}];
dsj = FullSimplify[D[ri, sj],
Assumptions -> {Element[{si, sj}, Reals]}];

signalFunc[{SPi_, SPj_}] :=
NArgMax[{ri, dsi == 1, dsj == 1}, {si, sj}];

signalFunc[{0.8, 1.5}];

-
 It's some form of evaluation semantics mishmosh. Can do it either as signalFunc[{SPi1_, SPj1_}] := NArgMax[{ri, dsi == 1, dsj == 1} /. {SPi -> SPi1, SPj -> SPj1}, {si, sj}] or signalFunc[{SPi1_, SPj1_}] := Block[{SPi = SPi1, SPj = SPj1}, NArgMax[{ri, dsi == 1, dsj == 1}, {si, sj}]]. Note that this will be difficult; I get a warning that the constraints are not satisfied. – Daniel Lichtblau Dec 20 '12 at 0:26 Do you think the equations need to be written in full inside the NArgMax? I still get an error there – Cameron Murray Dec 20 '12 at 1:09 If either SPi or SPj do not have values, then NArgMax is being asked to optimize a symbolic expression, which it cannot do. – whuber Dec 20 '12 at 2:44 The function takes SPi and SPj as arguments - is that not sufficient? I think that is Daniel's point. If I put the full equations inside NArgMax' I get the error >NArgMax::nosat: Obtained solution does not satisfy the following constraints within Tolerance -> 0.001: – Cameron Murray Dec 20 '12 at 3:32 D is a predefined MMA function to compute the derivative, so that expressions like D[ri, si] == 1 are (at best) meaningless. – whuber Mar 16 at 3:40

## closed as too localized by whuber, Verbeia♦Mar 16 at 10:31

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