About: Biconvex optimization

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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 .

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  • 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 argumentsis called a block multi-convex function.A functionis block multi-convexiff it is convex with respect to each of the individual argumentswhile holding all others fixed. (en)
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  • 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 . (en)
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  • Biconvex optimization (en)
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