Failure in initial nonlinear constraint function evaluation. FMINCON cannot continue.

I have write the main program, an objective function and the non-linear constraint. My objective was to minimise V value in COST.m function by passing three decision variables , x0(1), x0(2) and x0(3). Could anyone please advice me?

The main program

clear
clc
data = xlsread("RCbeamdata.xls");
c         = data(1,1) % Nominal cover (mm) 
mainD     = data(2,1) % Main rebar diameter (mm)
mainLink  = data(3,1) % Link diameter (mm)
fck       = data(4,1) % Characteristic strength of concrete (MPa)
fyk       = data(5,1) % Characterisc strength of steel (MPa)
Rc        = data(6,1) % Rate for concrete (RM/m3)
Rs        = data(7,1) % Rate for steel (RM/kg)
rhos      = data(8,1) % Density of steel (kg/m3)
L         = data(9,1) % Span of beam (m)
M         = data(10,1) % Maximum moment (kNm)
V         = data(11,1) % Maximum shear force (kN)
% Starting point for optimization (decision variables)
x0(1)    = data(12,1) % starting beam width (mm)
x0(2)    = data(13,1) % starting beam height (mm)
x0(3)    = data(14,1) % starting tensile reinforcement areas (mm2)
%x0(4)    = data(15,1) % starting compression reinforcement areas (mm2)
% Min and max ratio of reinforcement
fctm     = 0.3*fck^(2/3);
rho_min  = max(0.26*fctm/fyk, 0.0013); %Asmin requirement
rho_max  = 0.04;  %As max requirement
d = x0(2)- c- mainLink-0.5*mainD; %Effective depth 
Mult = 0.167*fck*x0(1)*d^2; % Ultimate moment of resistance for a singly reinforced beam
% Constraint
A = [];
b = [];
Aeq = [];
beq = [];
lb = [ 0.3*x0(2),x0(2),0.5*pi*mainD^2 ];
ub = [ 0.6*x0(2),x0(2),0.04*x0(1)*x0(2) ];
% Nonlinear constraint
% nonlincon =@(x) SinglyRCBeamConstraint(x0,fyk,fck,d,M,V,rho_min);
% options = optimoptions(@fmincon,'algorithm','sqp','Display','final-detailed',...
%                        'ConstraintTolerance',1e-8,'MaxFunctionEvaluations',5000,...
%                        'MaxIterations',2000,'OptimalityTolerance',1e-6);
%[c,ceq] = nonlincon(x0);

%Define problem
% problem =createOptimProblem('fmincon','x0',x0,'objective',RCCOST,'lb',lb,'ub',ub,...
%                       'nonlcon',SinglyRCBeamConstraint,'options',options);
% 
% %fmincon SOLVER
% % [x,fval,eflag,output] = fmincon(problem);
% 
% %Global search solver
% gs = GlobalSearch('Display','final','FunctionTolerance',0,'NumTrialPoints',400000,...
%                   'NumStageOnePoints',8000)
% 
% rng default
% [xg,fg,exitflag,output,solutions] = run(gs,problem)
fun = @(x0) COST(x0,Rc,Rs,rhos,L);
x0 = lb;
[x,fval] = fmincon(fun,x0,A,b,Aeq,beq,lb,ub,@SinglyRCBeamConstraint)

The OBJECTIVE FUNCTION

function V = COST(x,Rc,Rs,rhos,L)
% Objective function

V = (Rc*(x(1)*x(2) -x(3)) + Rs*x(3)*rhos)*L;
end

The NONLINEAR CONSTRAINT

function [c,ceq] = SinglyRCBeamConstraint(x0,fyk,fck,d,M,V,rho_min)
gamma_s = 1.15;
gamma_c = 1.5;
y= (5000/1173)*(fyk/fck);
x= y*(x0(3)/(x0(1)*d))-1; % Neutral axis depth for singly reinforced concrete
c(1) = (5000/1173)*(fyk/fck)*(x0(3)/(x0(1)*x0(2)))-1;  % x <=0.45d (Avoid Brittle Failure)
c(2) = M*1e6/(17/(258*gamma_c)*fck*x0(1)*x*(d-0.4*x))-1;  % Mmax <=Mult due to compression force in concrete
c(3) = M*1e6/((fyk/gamma_s)*x0(3)*(d-0.4*x))-1;              % Mmax <= Mult due to tension force in steel
c(4) = V*1e3/((0.18*(1-fck/250)*fck)*x0(1)*d)-1;          % Vmax <= Vrdc(45)
c(5) = 1-(x0(3)/(rho_min*x0(1)*d));                   % As >=Asmin
ceq = [];
end

Answer 1

[Torsten]

You forgot to include "RCbeamdata.xls".

And you know that you fix x(2) to x0(2) if you set lb(2) = ub(2) = x0(2) ?

And you must parametrize "SinglyRCBeamConstraint" in the same way as you did for "COST":

obj = @(x) COST(x,Rc,Rs,rhos,L);
nonlcon = @(x)SinglyRCBeamConstraint(x,fyk,fck,d,M,V,rho_min);
[x,fval] = fmincon(obj,x0,A,b,Aeq,beq,lb,ub,nonlcon)