Maximum likelihood and optimization

Hello, i'm trying to minimize a function of 15 variables. The function reproduce this model https://poseidon01.ssrn.com/delivery.php?ID=126024068112006091070127068116100098039053020046074058007068114088085114006090005108037124118022010007121002125118097068098070012058074010000092112092122022103124110056019033081104111072097065122000004021106098097003101093107107007121024103087112125126&EXT=pdf

I would like to try to use maximum likelihood, could it be helpful? This is the code of my function.

function [SQ_TOT] = Myobjectivefunction(Param,DatiDish,t)
DUM=DatiDish(1:4,:);
DUMqA=[Param(5:8)];
expbeta=exp(DUMqA*DUM);
t1=t.^Param(4);
t2=t.^Param(4);
t2(length(t))=[];
t2=[0 t2];
tc=t1-t2;
lt=length(t);
cohort=zeros(1,lt);
for i=1:length(t1);
  summ=[zeros(1,i-1) expbeta(i:lt).*tc(1:lt+1-i)];
  cohort=[cohort;summ];
end;
cohort(1,:)=[];   
F_A=(1-(Param(3)./(Param(3)+cumsum(cohort,2))).^Param(2)).*(1-Param(1));

DUMqR=[Param(12:15)];
expbeta_R=exp(DUMqR*DUM);
t1R=t.^Param(11);
t2R=t.^Param(11);
t2R(length(t))=[];
t2R=[0 t2R];
tc_R=t1R-t2R;
cohort_R=[];
for i=1:length(t1);
  summ=[zeros(1,i-1) expbeta_R(i:length(t1)).*tc_R(1:length(t)+1-i)];
  cohort_R=[cohort_R;summ];
end;
cohort_R(1,:)=[];
%HEY_R=cumsum(cohort_R,2);
F_R=(1-(Param(10)./(Param(10)+cumsum(cohort_R,2))).^Param(9));
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%Addition%%%%
housed=DatiDish(5,:);
HouseCha1=housed;

housed(end)=[];
HouseCha2=[0 housed];
ChaninPop=HouseCha1-HouseCha2;
 
F_AZ=[zeros(lt,1) F_A];
EXP_A=[];
EXP_AA=[];
EC_RVERO=zeros(1,lt);
EC=[];
F_RZ=[zeros(lt-1,1) F_R];
F_AZ(:,end)=[];
F_RZ(:,end)=[];
ChaninPopR=ChaninPop(1:end-1);
EC_RVERO=[0];
for i=1:lt
EXP_AA=(F_A-F_AZ).*(ChaninPop+EC_RVERO)';
EC=sum(EXP_AA);
EC(lt)=[];
EXP_RR=(F_R-F_RZ).*(EC)';
EC_RVERO=sum(EXP_RR);
EC_RVERO=[0 EC_RVERO];
EC_RVERO(end)=[];
end
EC=[EC sum(EXP_AA(:,end))];
EC_RVERO(1)=[];
EC_RVERO=[EC_RVERO sum(EXP_RR(:,end))];  
EC3m_R=[0 0];
for i=3:lt;
    summ=sum(EC_RVERO(i-2:i));
    EC3m_R=[EC3m_R summ];
end;
EC3m=[EC(1) sum(EC(1:2))];
for i=3:lt;
    summ=sum(EC(i-2:i));
    EC3m=[EC3m summ];
end;
ADD=DatiDish(6,:);
DIV_=ADD~=0;
DIVEC3=DIV_.*EC3m;
DIV_A=(DIVEC3-ADD);
DIV_A2=(DIV_A).^2;
SQ_ADD=sum(DIV_A2(1,:));
LOSS=DatiDish(7,:);
DIV=LOSS~=0;
DIV_L=DIV.*EC3m_R;
DIV_LOSS=(DIV_L-LOSS);
DIV_LOSS2=(DIV_LOSS).^2;
SQ_LOSS=sum(DIV_LOSS2(1,:));
EXP_E=EC-EC_RVERO;   
EXP_END=cumsum(EXP_E);
END=DatiDish(8,:);
DIV1=END~=0;
DIV2=DIV1-DIV_;
DIV_E=DIV2.*EXP_END;
END_DIV=DIV2.*END;
DIV_E(1)=EXP_END(1);
SQ_EN=[(EXP_END(1))^2];
pos=find(DIV2==1);
for i=4:3:pos(length(pos));
DIV_END=((DIV_E(i)-DIV_E(i-3))-(END_DIV(i)-END_DIV(i-3)))^2;
SQ_EN=[SQ_EN DIV_END];
end;
SQ_END=sum(SQ_EN(1,:));
SQ_END=SQ_END+(END(length(END))-EXP_END(length(EXP_END)))^2;
SQ_TOT=SQ_LOSS+SQ_END+SQ_ADD

end

the inputs are:

DATANEFLIX12=[0	0	0	0	0	0	1	1	1	0	0	0	0	0	0	0	0	0	1	1	1	0	0	0	0	0	0	0	0	0	1	1	1	0	0	0	0	0	0	0	0	0	1	1	1	0	0	0	0	0	0	0	0	0	1	1	1	0	0	0	0	0	0	0	0	0	1	1	1	0	0	0	0	0	0	0	0	0	1	1	1	0	0	0	0	0	0	0	0	0	1;
0	0	0	0	0	0	0	0	0	1	1	1	0	0	0	0	0	0	0	0	0	1	1	1	0	0	0	0	0	0	0	0	0	1	1	1	0	0	0	0	0	0	0	0	0	1	1	1	0	0	0	0	0	0	0	0	0	1	1	1	0	0	0	0	0	0	0	0	0	1	1	1	0	0	0	0	0	0	0	0	0	1	1	1	0	0	0	0	0	0	0;
1	1	1	0	0	0	0	0	0	0	0	0	1	1	1	0	0	0	0	0	0	0	0	0	1	1	1	0	0	0	0	0	0	0	0	0	1	1	1	0	0	0	0	0	0	0	0	0	1	1	1	0	0	0	0	0	0	0	0	0	1	1	1	0	0	0	0	0	0	0	0	0	1	1	1	0	0	0	0	0	0	0	0	0	1	1	1	0	0	0	0;
0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0;
5675528	5681982	5688437	5694891	5701345	5707799	5714253	5720707	5727162	5733616	5740070	5746524	5752978	5759450	5765921	5772392	5778863	5785335	5791806	5798277	5804748	5811220	5817691	5824162	5830633	5837109	5843585	5850061	5856536	5863012	5869488	5875964	5882440	5888915	5895391	5901867	5908343	5914812	5921282	5927752	5934222	5940692	5947161	5953631	5960101	5966571	5973041	5979510	5985980	5957108	5928235	5899362	5870490	5841617	5812744	5783872	5754999	5726127	5697254	5668381	5639509	5681982	5688437	5694891	5701345	5707799	5714253	5720707	5727162	5733616	5740070	5746524	5718660	5759450	5765921	5772392	5778863	5785335	5791806	5798277	5804748	5811220	5817691	5824162	5798380	5837109	5843585	5850061	5856536	5863012	5869488;
0	0	0	745	0	0	3479	0	0	2011.93000000000	0	0	2551.30000000000	0	0	3670.21000000000	0	0	4761.52700000000	0	0	2387.07600000000	0	0	3404.50200000000	0	0	4527.26100000000	0	0	5858.15200000000	0	0	3151.69600000000	0	0	4005.77600000000	0	0	5240.31200000000	0	0	6668.32800000000	0	0	4696.71300000000	0	0	5006.06200000000	0	0	6602.51300000000	0	0	8780.65300000000	0	0	4287.08900000000	0	0	5459.29600000000	0	0	7977.22800000000	0	0	7589.34000000000	0	0	7126.43800000000	0	0	7561.93600000000	0	0	9221.57500000000	0	0	11024.1000000000	0	0	8424.55000000000	0	0	9176.85000000000	0	0	12097.5500000000	0	0	12946.2160000000;
0	0	0	645	0	0	648	0	0	732.930000000000	0	0	771.300000000000	0	0	797.210000000000	0	0	880.527000000000	0	0	993.076000000000	0	0	1033.50200000000	0	0	1102.26100000000	0	0	1160.15200000000	0	0	1291.69600000000	0	0	1343.77600000000	0	0	1418.31200000000	0	0	1525.32800000000	0	0	1609.71300000000	0	0	1693.06200000000	0	0	1782.51300000000	0	0	1912.65300000000	0	0	2098.08900000000	0	0	2077.29600000000	0	0	2165.22800000000	0	0	2316.34000000000	0	0	2453.43800000000	0	0	2574.93600000000	0	0	2600.57500000000	0	0	2766.10000000000	0	0	2972.55000000000	0	0	3108.85000000000	0	0	3260.55000000000	0	0	3342.21600000000;
21500	0	0	21600	0	0	24431	0	0	25710	0	0	27490	0	0	30363	0	0	34244	0	0	35638	0	0	38009	0	0	41434	0	0	46132	0	0	47992	0	0	50654	0	0	54476	0	0	59619	0	0	62706	0	0	66019	0	0	70839	0	0	77707	0	0	79896	0	0	83278	0	0	89090	0	0	94363	0	0	99036	0	0	104023	0	0	110644	0	0	118902	0	0	124354	0	0	130422	0	0	139259	0	0	148863];

ti=[1/3:1/3:30+1/3];

So if i want to call the function to minimize it for example with fminsearch, i have to write:

fun=@(Param) Myobjectivefunction(Param,DATANETFLIX12,ti)

The problem is that with traditional optimization method like fminsearch i don't reach the real absolute minimum and i'm far from it. If there is another method to find global minimum (different from maximum likelihood) it's all the same!

Please it's very importante for me, thank you very much!