Biconvex optimization is a generalization of convex optimization where the objective function and the constraint set can be biconvex. There are methods that can find the global optimum of these problems.
A set is called a biconvex set on if for every fixed , is a convex set in and for every fixed , is a convex set in .
A function is called a biconvex function if fixing , is convex over and fixing , is convex over .
A common practice for solving a biconvex problem (which does not guarantee global optimality of the solution) is alternatively updating by fixing one of them and solving the corresponding convex optimization problem.
The generalization to functions of more than two arguments is called a block multi-convex function. A function is block multi-convex iff it is convex with respect to each of the individual arguments while holding all others fixed.
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- Floudas, Christodoulos A. (2000). Deterministic global optimization : theory, methods, and applications. Dordrecht [u.a.]: Kluwer Academic Publ. ISBN 978-0-7923-6014-8.
- Chen, Caihua (2016). ""The direct extension of ADMM for multi-block convex minimization problems is not necessarily convergent"". "Math. Prof.". 155: 57–59. doi:10.1007/s10107-014-0826-5.
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