Fsolve error: relative norm of the current step is less than max(option​s.StepTole​rance^2,ep​s) = 1.000000e-12

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Amina Enkhbold
Amina Enkhbold 2020-4-12
评论： Yulun Wu 2021-12-8
Hello everyone,
I am running the following code, however, I observe an error:
fsolve stopped because the relative norm of the current step, 7.033578e-13, is less than
max(options.StepTolerance^2,eps) = 1.000000e-12. However, the sum of squared function
values, r = 3.409018e+18, exceeds sqrt(options.FunctionTolerance) = 1.000000e-03.
Optimization Metric Options
relative norm(step) = 7.03e-13 max(StepTolerance^2,eps) = 1e-12 (default)
r = 3.41e+18 sqrt(FunctionTolerance) = 1.0e-03 (default)
function F = new(x);
kap_dep = 0.0036;
kap_div = 0.0012;
thetam = 3.53;
mtgparam = thetam/(thetam-1);
thetad = - 1.46;
depparam = thetad/(thetad-1);
div_bar = 9;
chi_saver = 0.601;
log_refi_rate = -3.282968022102128;
log_non_am_share = -0.004357084122431;
log_new_loan_size = 0.484804774865286;
log_nu_t = -0.012277614667639;
log_debt = 0.212443935354230;
log_mstar_bank = 0.193437105171249;
mbank = exp(3.204035192501455);
log_y = -0.033219520228313;
log_ph = -0.282925342335558;
log_h_saver = 1.742131415613060;
log_R_new = 0.015649702109572;
log_inflation_factor = -0.007920530545208;
log_Lam_saver_debt = 0.448184815036209;
log_Lam_saver_0_inv = 0.463834545296377;
Rdep = depparam*(exp(log_R_new)-kap_dep);
log_R_dep = log(depparam*(exp(log_R_new)-kap_dep));
log_pay_bank = 3.300154738807201;
log_m_bank = 3.204035192501455;
F(1) = exp(log_refi_rate) * (exp(x(5)) + (1.0-exp(log_non_am_share)))* exp(log_new_loan_size) +exp(log_nu_t)*x(1)*(1.0-exp(log_refi_rate)) + exp(log_refi_rate)*exp(log_nu_t)*exp(log_debt) - x(1);
F(2) = exp(log_mstar_bank)*(exp(x(5)) - exp(log_non_am_share))+ (1.0 - exp(log_refi_rate))*x(2)*exp(log_nu_t)+ exp(log_refi_rate)*exp(log_nu_t)*exp(mbank) - x(2);
F(3) = exp(log_y) + exp(x(4)) - del*exp(log_ph)*exp(log_h_saver) + (Rdep+kap_dep)*exp(log_inflation_factor)*x(3) - x(3);
F(4) = log(exp(log_inflation_factor)*(exp(log_pay_bank) -exp(log_R_new)*exp(log_m_bank) - exp(log_mstar_bank) + (exp(log_R_new) - exp(log_R_dep) - kap_dep)*chi_saver * x(3)) - kap_div*0.5*(exp(x(4)) - div_bar).^2) - x(4);
F(5) = log(mtgparam*(1.0/x(6) + exp(log_non_am_share) - x(7)/x(6))) - x(5);
F(6) = exp(log_Lam_saver_debt)*(x(6)/exp(log_Lam_saver_0_inv)*exp(log_non_am_share)*(1.0 -exp(log_refi_rate)) + 1.0/(1.0 + kap_div*(exp(x(4))-div_bar))) - x(6);
F(7) = exp(log_Lam_saver_debt)*(x(7)/exp(log_Lam_saver_0_inv)*exp(log_non_am_share)*(1.0 -exp(log_refi_rate))+exp(log_refi_rate)*exp(log_non_am_share)*x(6)/exp(log_Lam_saver_0_inv)+1.0/(1.0 + kap_div*(exp(x(4))-div_bar))-(1.0/((1.0 + kap_div*(exp(x(4))-div_bar))*exp(log_Lam_saver_0_inv)))*exp(log_R_new)*exp(log_inflation_factor)) - x(7);
Then I run
x0=rand(1,7);
x=fsolve(@new,x0)
I looked at other documentations and tried options. Could you tell me or provide guidance on how to approach this problem? Thanks.
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Walter Roberson
Walter Roberson 2021-12-8
@Yulun Wu
Alex Sha uses the commercial package at http://www.7d-soft.com/en/
Alex has posted a number of excellent results from the package over the years. I am sometimes able to do slightly better, but it takes me hours to do better than what Alex can do in a few minutes.
However, the software is not inexpensive. I think the price is probably worth it for people who do a lot of optimization... but I would not be able to justify it for myself, for example.

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