Home Generating random starting points in n-dimension for fmincon algorithm - uniform distribution of space
 I am using fmincon in Matlab to minimize a smooth yet highly non-linear objective function. My problem is in n-dimension, with n>250 in some instances. I have found that using different starting points improves dramatically the solution, as can be expected from an objective function with multiple local minima. I have used haltonset to generate quasi random starting point in the n dimensional hypercube, which I then rescale into the n-dimensional hyperspace defined by the lower and upper bounds of my problem. I am however unsure of whether I am covering the space of possible solutions (defined by lower and upper bounds) in a sufficiently uniform manner. It could come from 2 issues: 1) the initial generation of the quasi random points is not "dense" enough, 2) the rescaling could create holes in the hyperspace because of bounds that are highly different Is there a way that I can ensure that my starting points cover my space adequately (maybe specify the maximum distance between my starting points in n-dimension). Thank you for your help See below code I am using: objective_list = containers.Map('KeyType','int32','ValueType','any'); initial_pt_list = containers.Map('KeyType','int32','ValueType','any'); optimal_pt_list = containers.Map('KeyType','int32','ValueType','any'); net_size=100; [variable_size, ~]=size(initial_pt); p=haltonset(variable_size,'Skip',1e3,'Leap',1e2); p = scramble(p,'RR2'); X0 = net(p,net_size); for net0 = 1:1:net_size temp_unit_vector= X0(net0,:); temp_initial_pt = lower_b + temp_unit_vector'.*(upper_b - lower_b); initial_pt_list(net0)=temp_initial_pt; end