Finding the right solver - matlab

Question

I need to solve the following non-linear problem with constraints but I am not sure to use the appropriate function and solver as changing from the algorithm: 'interior-point' to 'sqp' give different answers. Could you help first to make sure fmincon is the most appropriate function here and also if the options should be set up in a different way to ensure that the optimization does not stop too early. I have tried to set up: 'MaxFunctionEvaluations' to 1000000 and 'MaxIterations'to 10000 and this helps but the time required increases as well dramatically.
w is a vector whose values have to be optimized.
scores is a vector of the same size as w.
the size if w and scores is usually between 10 and 40.
Here is the optimization setup:
objective function: sum(log(abs(w)));
linear inequalities1: w_i > 0 if scores_i > 0
linear inequalities2: w_i < 0 if scores_i < 0
non-linear equalities1: sum(abs(w)) = 1
non-linear inequalities1: sqrt(w * sigma * w') <= 0.1
Here is my code:
N = numel(scores);
%%%LINEAR EQUALITIES CONSTRAINTS
Aeq = [];
beq = [];
%%%LINEAR INEQUALITIES CONSTRAINTS
temp = ones(0,N);
temp(scores >= 0) = -1;
temp(scores < 0) = 1;
A = diag(temp);
b = zeros(N,1);
%%%BOUNDs CONSTRAINTS
lb = [];
ub = [];
w0 = ones(1,N)/N;
nonlcon = #(w)nonlconstr(w,sigma,tgtVol);
options = optimoptions('fmincon','Algorithm','interior-point','MaxFunctionEvaluations',1000000,'MaxIterations',10000);
%options = optimoptions('fmincon','Algorithm','interior-point','OptimalityTolerance',1e-7);
[w,fval,exitflag,output] = fmincon(#(w)objectfun(w),w0,A,b,Aeq,beq,lb,ub,nonlcon,options);
function [c,ceq] = nonlconstr(w,sigma,tgtVol)
c = sqrt(w*sigma*w') - tgtVol;
ceq = sum(abs(w)) - 1;
end
function f = objectfun(w)
f = sum(-log(abs(w)));
end