# Minimization of the sum of convex function and non-linear non convex function

I'm trying to minimize the unconstrained scalar sum of a quadratic convex function (to which a convex optimizer is readily applied) and a non-linear and non-convex function which is differentiable.

General purpose non-linear optimizers are not providing adequate results, which I assume is due to the high dimensionality of my problem (>=10000), so I was wondering if there was a better way to go about minimizing my function given that it is decomposable into a convex and differentiable non convex part.

• Is the non-convex part concave? There are specialized methods for minimizing functions that are the difference of two convex functions (or the sum of a convex function and a concave function.) – Brian Borchers Apr 26 '16 at 15:10
• Unfortunately it isn't. It's basically the square of the difference of two normalized (with a factor added so that no singularities are present) dot products of my "target" vector with different data points – grizzlyjoker Apr 26 '16 at 15:42