Convex optimization ii

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.

Course description Subgradient, cutting-plane, and ellipsoid methods. Decentralized convex optimization via primal and dual decomposition. Monotone operators

Is 0 a quasiconvex optimization problem?

0is quasiconvex instead of convex, we say the problem (4

15) is a (standard form) quasiconvex optimization problem

Since the sublevel sets of a convex or quasiconvex function are convex, we conclude that for a convex or quasiconvex optimization problem the ǫ-suboptimal sets are convex

In particular, the optimal set is convex

What is a convex bound in global optimization?

(See, e g , exercise 11 23

) Bounds for global optimization Many methods for global optimization require a cheaply computable lower bound on the optimal value of the nonconvex problem

Two standard methods for doing this are based on convex optimization

In relaxation, each nonconvex constraint is replaced with a looser, but convex, constraint

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