Why convex optimization

  • Optimization book

    For example, the feasible region of every linear program is convex.
    To see this, first suppose there is only one constraint, which is an inequality.
    Then the feasible region is just a half-space, which is clearly convex.
    The feasible region of a linear program is an intersection of such half-spaces..

  • Why are convex optimization important?

    Convex optimization solution is crucial due to the many useful qualities that make it straightforward to solve and study.
    For instance, in the case of convex optimization problems, the optimal solution is guaranteed to exist in the form of a global minimum..

  • For example, the feasible region of every linear program is convex.
    To see this, first suppose there is only one constraint, which is an inequality.
    Then the feasible region is just a half-space, which is clearly convex.
    The feasible region of a linear program is an intersection of such half-spaces.
Convex optimization problems are far more general than linear programming problems, but they share the desirable properties of LP problems: They can be solved quickly and reliably up to very large size -- hundreds of thousands of variables and constraints.

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