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I am solving the following biconvex problem: $$\min_{x,y} f(y)$$ $$s.t. ~~ g(x) \leq 0$$ $$~~~~~h(x,y) = 0$$ $$x \in X, y \in Y$$ where $X$ and $Y$ are compact convex sets, $g(x)$ and $f(y)$ are convex and $h(x,y)$ is affine for fixed $x$ or $y$. I wonder if there is any efficient algorithm to solve this type of optimization problem, not restricted to algorithms for general biconvex optimization problems.

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