Why is the duality gap zero for non convex quadratic programming with a single constraint?

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From what I read here Convex Optimization, Appendix B and Perfect Duality §2.3, strong duality holds for quadratic programs of the form: $$ \min_x x^\top Ax+x^\top a+\alpha \ni x^\top Bx+x^\top b+\beta\le 0 $$

I have some trouble understanding why.