Essentially, how can I check if functions like this are convex, and how can I know before I write a quadratic constraint that it will be convex? So essentially, how can I write feasible convex quadratic constraints so that I don't waste my time writing non-convex ones. Is there a certain form quadratic constraints look like in convex form? I am writing an optimization program that's mixed-integer and quadratic in constraints and objective function but am running into the issue of having a non-semidefinite matrix Q to be used in my solver. Some of the quadratic constraints I have are:
-x8*x10 + 1.4*x7*x9 <= 0 x7*x1 + x8*x4 <= 1470, "Rows Constraint" x9*x2 <= 163.128, "Seats Per Row Constraint First-Class" x10*x5 <= 163.128, "Seats Per Row Constraint Premium-Economy"
Which of the above are non-convex? Also, all x's are a positive number.
Thank you so much in advance! PS I am a master's of aerospace engineering student looking for help!