Nannan gives me a fold named "Matlab Help". On page 46 of "Optimization Toolbox User Guide", it lists the constrain and objective type, and the matlab function. For example, if the constrain is linear and the objective is quadratic, we can use quadprog. Note that it can not slove $D_1$ in Section 4.1 of "Smooth minimization of non-smooth functions". Problem: max ((X^T)HX) and H is positive semi definite. The matlab function "quadratic" can not solve this kind of problem. It can only solve the problem: min ((X^T)HX) and H is positive semi definite.