optimization problem with biaffine equality constraints

[Xinwei Shen]

Dear Prof. Johan

I faced a problem in below form

min f(x,y)
s.t.
g(x,y)<=0
h(x,y)=0

where 

f(x,y) is a quadratic function

g(x,y) is convex on both x and y, 

h(x,y)=0 is affine on x for each fixed y, and affine on y for each fixed x, and not in quadratic form on x and y.

I tried to solve this problem with Bmibnb in Yalmip (upper solver: IPOPT, lower solver: Gurobi). However, it didn't find even a local minimum (IPOPT did, when I assigned a good initial guess for it). 

My questions are:

1. Can I also assign a initial guess for Bmibnb to improve the convergence?

2. Do you have any other suggestions on how to solve this kind of problem?  I want to look for a method/algorithm with better convergence (maybe speed or better local minimizer) than conventional primal-dual interio-point method.

[Xinwei Shen]

For Q1, it's noteworthy that I set "usex0" as 1 in sdpsettings, but it did not improve the performance of Bmibnb. I don't know why.

[Johan Löfberg]

You would have to be way more specific than that (i.e. reproducible example needed)