absolute value in equality constraints

i would like to know how to write the absolute value in equality constraints.

var10(i) = var10(i-1) + (0.5/4500) * (ABS ( 0.25*var7(i) ) ) / var9(i)

my Input(i) is a vector with the length of 350*1 with positive integer values, that are measurements of a continuous variable.

prob = optimproblem;

% equality constrainst 
prob.Constraints.econs6 = optimconstr(N);    %Non linear with absoulte
prob.Constraints.econs6(1) = var10(1) == (0.5*(1/4500) * abs((var7(1) *0.25))) ./ var9(1);
prob.Constraints.econs6(2:N)= var10(2:N) == var10(1:N-1) + (0.5*(1/4500) * abs((var7(2:N)*0.25))) ./ var9(2:N); 

x0.var7 = zeros(size(N));   
x0.var9 = zeros(size(N));
x0.var10 = zeros(size(N)); 
[values,fval,exitflag,output] = solve(prob,x0,'Options',options); 

thanks in advance for hints.

Answer 1

[Walter Roberson]

N = 5;
var10 = optimvar('var10', N);
var9 = optimvar('var9', N);
var7 = optimvar('var7', N);

prob = optimproblem;
ABS = @(x) sqrt(x.^2);
% equality constrainst 
prob.Constraints.econs6 = optimconstr(N);    %Non linear with absoulte
thisconstraint = var10(1) == (0.5*(1/4500) * ABS((var7(1) *0.25))) ./ var9(1)

thisconstraint = 
  Nonlinear OptimizationEquality

    var10(1) == ((0.00011111 .* sqrt((var7(1) .* 0.25).^2)) ./ var9(1))

prob.Constraints.econs6(1) = thisconstraint

prob = 
  OptimizationProblem with properties:

       Description: ''
    ObjectiveSense: 'minimize'
         Variables: [1×1 struct] containing 3 OptimizationVariables
         Objective: [0×0 OptimizationExpression]
       Constraints: [1×1 struct] containing 1 OptimizationConstraint

  See problem formulation with show.

prob.Constraints.econs6(2:N)= var10(2:N) == var10(1:N-1) + (0.5*(1/4500) * ABS((var7(2:N)*0.25))) ./ var9(2:N); 

x0.var7 = zeros(N,1);   
x0.var9 = zeros(N,1);
x0.var10 = zeros(N,1); 
[values, fval, exitflag, output] = solve(prob, x0); 

Solving problem using fmincon.

Error using optim.problemdef.OptimizationProblem/solve
Nonlinear constraint function is undefined at initial point. Fmincon cannot continue.