How to minimize this function

Hello guys, i'm working for my university on this function. I have to minimize it. I have to get into a good part of the space before using a more traditional optimizer, like fminsearch. It was said that gradients are very helpful, but they need to be in a half-decent part of the space to be able to get started.

This is the code, thank you very much and let me know :D

I want to minimize SQ_TOT which is the SSE of my model with the real data. The model is Hazard proportional and use Weibull baseline.

function [SQ_TOT] = Myobjectivefunction(Param,DatiDish)
t=[1/3:1/3:30+1/3];%Param=[0.5254010 11.4402640 29861.1830810 2.0010250 -0.051606000 -0.057373000 0.036517000 -0.099394000 1.647586000 81.195773000 1.422753000 -0.078617000 0.036363000 0.106596000 0.128553000];
DUM=DatiDish(1:4,:);
%Param=Param(1:15);
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,:)=[];   
HEY_A=cumsum(cohort,2);
F_A=(1-(Param(3)./(Param(3)+HEY_A)).^Param(2)).*(1-Param(1));
%%%%Retention Model%%%%%
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=[];
%cohort_R= matrice riga 1000
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)+HEY_R)).^Param(9));
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%Addition%%%%
housed=DatiDish(5,:);
HouseCha1=housed;
%HouseCha1= riga 19 
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=[];
%EC= riga 976 oppure colonna IA e riga 1712 
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

Param (1x15) is the variable that i want to optimize, so i create the function:

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

This is the input of my function

DATANETFLIX12=[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; 
0.000	0.000	0.000	745.000	0.000	0.000	3479.000	0.000	0.000	2011.930	0.000	0.000	2551.300	0.000	0.000	3670.210	0.000	0.000	4761.527	0.000	0.000	2387.076	0.000	0.000	3404.502	0.000	0.000	4527.261	0.000	0.000	5858.152	0.000	0.000	3151.696	0.000	0.000	4005.776	0.000	0.000	5240.312	0.000	0.000	6668.328	0.000	0.000	4696.713	0.000	0.000	5006.062	0.000	0.000	6602.513	0.000	0.000	8780.653	0.000	0.000	4287.089	0.000	0.000	5459.296	0.000	0.000	7977.228	0.000	0.000	7589.340	0.000	0.000	7126.438	0.000	0.000	7561.936	0.000	0.000	9221.575	0.000	0.000	11024.100	0.000	0.000	8424.550	0.000	0.000	9176.850	0.000	0.000	12097.550	0.000	0.000	12946.216;
0.000	0.000	0.000	645.000	0.000	0.000	648.000	0.000	0.000	732.930	0.000	0.000	771.300	0.000	0.000	797.210	0.000	0.000	880.527	0.000	0.000	993.076	0.000	0.000	1033.502	0.000	0.000	1102.261	0.000	0.000	1160.152	0.000	0.000	1291.696	0.000	0.000	1343.776	0.000	0.000	1418.312	0.000	0.000	1525.328	0.000	0.000	1609.713	0.000	0.000	1693.062	0.000	0.000	1782.513	0.000	0.000	1912.653	0.000	0.000	2098.089	0.000	0.000	2077.296	0.000	0.000	2165.228	0.000	0.000	2316.340	0.000	0.000	2453.438	0.000	0.000	2574.936	0.000	0.000	2600.575	0.000	0.000	2766.100	0.000	0.000	2972.550	0.000	0.000	3108.850	0.000	0.000	3260.550	0.000	0.000	3342.216;
21500.000	0.000	0.000	21600.000	0.000	0.000	24431.000	0.000	0.000	25710.000	0.000	0.000	27490.000	0.000	0.000	30363.000	0.000	0.000	34244.000	0.000	0.000	35638.000	0.000	0.000	38009.000	0.000	0.000	41434.000	0.000	0.000	46132.000	0.000	0.000	47992.000	0.000	0.000	50654.000	0.000	0.000	54476.000	0.000	0.000	59619.000	0.000	0.000	62706.000	0.000	0.000	66019.000	0.000	0.000	70839.000	0.000	0.000	77707.000	0.000	0.000	79896.000	0.000	0.000	83278.000	0.000	0.000	89090.000	0.000	0.000	94363.000	0.000	0.000	99036.000	0.000	0.000	104023.000	0.000	0.000	110644.000	0.000	0.000	118902.000	0.000	0.000	124354.000	0.000	0.000	130422.000	0.000	0.000	139259.000	0.000	0.000	148863.000];
%

[Riccardo Bartoloni]

Please help

Answer 1

[Jeff Miller]

If the problem is to find good starting parameter values, then maybe you could start with a grid search over your parameter space to find some points that produce reasonably low SSE values. Then start fminsearch from one (or several) of those. If fminsearch is pretty fast on your problem, you could even generate starting parameter values randomly and save the best result across thousands of random starting points.