how to speed up a nonlinear convex problem if solved using fmincon

I have a nonlinear convex problem with a large number of variables (100*n_samples+66). For example, if n_samples=50, I have 5066 variables. I have a set of linear constraints and a set of nonlinear constraints. The nonlinear constraints are convex and the objective function is a linear function that has 66 variables. To get a solution, the optimizer terminated because it reached the maximum number of function evaluations which I set at 90000 (it took 13 hours for the optimizer to stop). This is a smaple of the iteration when n_samples=1, i.e., we have 166 variables. Any idea how to speed up the optimizer (i have matlab 2013a ).

First-order Norm of

Iter F-count f(x) Feasibility optimality step

871 149095 5.800103e+03 1.776e-15 1.469e+00 5.745e-01

872 149269 5.798809e+03 1.776e-15 1.444e+00 5.761e-01

873 149443 5.797519e+03 1.776e-15 1.444e+00 5.774e-01

874 149617 5.796233e+03 1.849e-15 1.444e+00 5.785e-01

875 149791 5.794949e+03 4.441e-16 1.444e+00 5.793e-01

876 149965 5.793668e+03 4.031e-15 1.444e+00 5.799e-01

877 150139 5.792388e+03 3.553e-15 1.444e+00 5.802e-01

878 150311 5.789831e+03 1.776e-15 1.444e+00 1.161e+00

879 150483 5.787275e+03 6.314e-16 1.444e+00 1.160e+00

880 150655 5.782154e+03 1.776e-15 1.444e+00 2.315e+00

881 150827 5.776978e+03 1.776e-15 1.444e+00 2.297e+00

882 151005 5.772331e+03 1.776e-15 1.316e+00 1.987e+00

883 151181 5.769920e+03 1.776e-15 1.136e+00 9.909e-01

884 151357 5.768691e+03 2.429e-15 1.053e+00 4.984e-01

885 151531 5.767452e+03 2.984e-15 9.999e-01 5.006e-01

886 151705 5.766207e+03 1.776e-15 9.999e-01 5.029e-01

887 151879 5.764957e+03 1.776e-15 9.999e-01 5.051e-01

888 152051 5.763706e+03 1.776e-15 9.999e-01 5.071e-01

889 152223 5.762454e+03 1.776e-15 9.999e-01 5.090e-01

890 152395 5.761203e+03 3.372e-15 9.999e-01 5.108e-01

891 152567 5.759954e+03 1.776e-15 9.999e-01 5.125e-01

892 152739 5.758708e+03 1.776e-15 9.999e-01 5.140e-01

893 152911 5.757463e+03 3.497e-15 9.999e-01 5.155e-01

894 153085 5.756221e+03 1.776e-15 9.999e-01 5.168e-01

895 153259 5.754981e+03 8.812e-16 9.999e-01 5.179e-01

896 153433 5.753743e+03 1.776e-15 9.999e-01 5.189e-01

[Piotr Balik]

Bumping the question, I have similar problem - convexity assumption should give a great boost