Bi-convex optimization

  • What is a bi convex function?

    Thereby, a function f : X \xd7 Y → R is called biconvex, if f(x,y) is convex in y for fixed xu220.

    1. X, and f(x,y) is convex in x for fixed yu220
    2. Y
      3. .Jun 22, 2007

  • What is a Biconvex function?

    Thereby, a function f : X \xd.

    1. Y → R is called biconvex, if f(x, y) is convex in y for fixed x ∈ X, and f(x, y) is convex in x for fixed y ∈ Y

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. by fixing one of them and solving the corresponding convex optimization problem.
is said to be a biconvex optimization problem or biconvex for short, if the feasible set B is biconvex on X × Y , and the objective function f is biconvex on B. Different from convex optimization problems, biconvex problems are in general global optimization problems which may have a large number of local minima.
Biogeography-based optimization (BBO) is an evolutionary algorithm (EA) that optimizes a function by stochastically and iteratively improving candidate solutions with regard to a given measure of quality, or fitness function.
BBO belongs to the class of metaheuristics since it includes many variations, and since it does not make any assumptions about the problem and can therefore be applied to a wide class of problems.

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Non-convex linear optimization
Convex optimization minimization algorithm