Chris Conlon

Some helpful links

Armadillo C++: This is a great C++ linear algebra library that has MATLAB like syntax.
KNITRO: This is probably the most reliable continuous optimization package and it works with MATLAB
MINLP: In the unfortunate case that your problem is not continuous MINLP works well for nonlinear integer optimization.
AMPL: is a modelling language that is able to compute first and second derivatives automatically, which is helpful for prototyping.
GNU Scientific Library (GSL): An extensive C library for scientific computing (matrices,statistical distributions, numerical integration, etc.)
Intel MKL: This is C/FORTRAN library that's highly optimized for specific architectures. It includes a LAPACK/BLAS implementation. It's not super easy to use, but sometimes you need a billion lognormals.
Sparse Grids Heiss and Winschel (2007) have posted code to generate sparse grids for quadrature online (and some results for multinomial choice problems).